However, RBS is not the only financial institution restricting deals in this way. An increasing number of providers are marketing special offers linked to their current accounts in an attempt to entice new current account custom and 'reward' existing customers.
Nationwide, for example, has just launched a leading personal loan with a typical interest rate of 7.9% - but again you can only borrow at this rate if you have a Nationwide current account.
But are these offers true rewards for loyalty or would you be better taking out additional products from other banks or building societies? We take a look at the leading current account providers to see what they have to offer.
RBS/Natwest
As well as limiting its credit cards to existing customers, RBS/Natwest offers packages of benefits, including roadside assistance and travel insurance, to current account customers - for a monthly fee. You can choose from Advantage Blue (or Royalties with RBS) at £6.95, Advantage Gold (or Royalties Gold with RBS) at £12.95 and, if you are a high earner, Advantage Private at £19.95.
These deals are only worthwhile if you are going to make use of all the benefits, though. Otherwise you should shop around for stand-alone deals.
When it comes to the cards on offer, the NatWest and RBS Platinum card has a 15-month interest-free period on balance transfers - one of the leading deals on the market. There is a 2.9% balance transfer fee and the standard rate of interest is 16.9%. Avoid using the card for spending on as well, as the 0% deal on purchases lasts just three months, after which you'll be charged the standard rate of interest on any purchases you've made.
This can only be beaten by the Virgin Credit Card, which has a 16-month 0% period on balance transfers. The transfer fee on this card is slightly higher at 2.98%, although the standard rate of interest is marginally lower at 16.6%. As with the RBS and NatWest cards, the 0% offer on purchases only runs for three months, so avoid using it for this purpose.
However, if you aren't looking to transfer a debt over from another card, a long interest-free period is irrelevant. Instead, if you're the type of person who pays your credit card off in full each month, consider a card that rewards you for spending.
The American Express Platinum Cashback card is the market leader. It pays 5% cashback for the first three months (up to a maximum spend of £2,000). You then earn 0.5% on the next £3,500 spent on the card, 1% on spending between £3,500 and £7,500 and 1.25% on any spending above £7,500.
HSBC
HSBC's Bank Credit Card is also only available to current account customers. Like RBS and Natwest's Platinum cards, it has a 15-month interest-free period for balance transfers. The transfer fee is the same at 2.9%, as is the standard rate of interest at 16.9%. Again, the interest-free period on purchases is just three months.
Therefore, while this is a good credit card and one well worth considering if you're looking to make a balance transfer, there are other alternatives: the Virgin Card for balance transfers, and the American Express Platinum card if you clear your balance each month.
Another option, if you're looking for a card that has a long interest-free period on purchases and balance transfers is the Sainsbury's Finance Credit Card - it offers 10 months interest-free for both. You also earn Nectar points each time you use this card for spending.
HSBC current account customers also have access to its market-leading Regular Saver account, which is paying a rate of 8.0% that is fixed for a year - you can pay in between £25 and £250 a month. This is far better than any other regular saver currently available, so worth taking advantage of if you can.
The bank is also trying to attract new current account customers by offering a £50 switching incentive to those who apply before 18 October. However, the downside of its standard current account is that you earn no interest on balances in credit.
Lloyds TSB
Lloyds has tried to entice new current account custom by offering add-ons to its Classic account.
One option is to add Vantage, which is available to anyone paying in at least £1,000 a month - as long as they stay in credit all the time. The advantage is higher credit interest rates, of up to 4% on balances between £5,000 and £7,000, although those with between £1 and £1,000 in their account receive just 0.1%.
If you keep between £5,000 and £7,000 in your current account this is a market-leading option. If your average balance is less than that there are better deals available.
Lloyds TSB's current account customers have access to its Incentive Saver account paying 3.04%. This is a highly competitive rate but there are some catches: you don't earn any interest in any month a withdrawal is made and no interest is paid on balances above £50,000. Also, after a year your money is transferred into the Easy Saver account which has a less competitive interest rate of 1.60%.
While the rate is undoubtedly competitive, Citibank's Flexible Saver Issue 6 pays a slightly higher rate of 3.30% and it is more flexible as unlimited penalty-free withdrawals are allowed.

Barclays
Barclays current account customers can get a Barclayloan Plus, but with a typical rate of 10.9% on £5,000 to £25,000 this does not look like much of an advantage. Alliance & Leicester and Blackhorse Finance can both easily beat this rate at 8.7% and 7.9% respectively (although it is worth noting that the Blackhorse Loan is secured against your home).
Alliance & Leicester
Alliance & Leicester, which is owned by Santander, the Spanish Bank that also owns Abbey, is one of the most aggressive when it comes to trying to build its current account market share. As such it has some of the most competitive current account offerings available.
New customers who move to the A&L Premier Account receive £100 cashback (as long as they transfer their direct debits over) and free European travel insurance. They also have exclusive access to the linked PlusSaver account although that's nothing to shout about - it's paying just 0.1% so you'd be much better off with A&L's Online Saver Issue 6, which is paying 3.0%, or even better, Citibank's Flexible Saver Issue 6 at 3.30%.
A&L also offers a highly competitive overdraft - it's interest free up to £2,000 for the first year. Thereafter you are charged 50p per day but this is capped at £5 per month.
Halifax
The Halifax Reward account is one of the most competitive current accounts in the market if you keep your balance in credit. You must pay in at least £1,000 but you have £5 a month credited to your account (this is instead of an annual interest rate).
Customers who pay £1,000 or more into their Halifax current account, or have the Halifax Ultimate Reward account (which costs £12.50 a month), qualify for the Halifax Extras deals.
These include a credit card offering 0% for 12 months on purchases and nine months at 0% on balance transfers (with a 3% transfer fee), after which the rate jumps to 17.9%. The introductory offer beats the market-leading All In One card, also from Halifax, which is currently offering nine months interest-free on both balance transfers and purchases.
Another benefit that could appeal to someone trying to get their first foot on the housing ladder is that current account customers can get a Halifax mortgage with a deposit of just 10%.
However, the Extras savings offer has a rate of 2.60%, which does not stand up so well to the competition. This includes Citibank's Flexible Saver Issue 6 at 3.30%.
Nationwide
Britain's biggest building society is offering current account customers a special low loan rate of 7.9% on amounts of between £7,500 and £14,999. This is a market-leading rate for an unsecured loan.
While not market leading in terms of the interest rate, the Flexaccount - the name of Nationwide's current account - is a good option if you travel abroad frequently, as its debit card is the cheapest to use overseas.
Abbey
The Abbey Account has two guises: one with a preferred in-credit rate and the other with a preferred overdraft rate. The preferred in-credit version offers a competitive 6% for the first 12 months on up to £2,500 but charges 19.9% on arranged overdrafts, while the overdraft version has a 12-month interest-free overdraft facility. A rate of 12.9% is charged after that time and in-credit balances up to £2,500 earn 0.5%.
It also has a linked loan offer with a typical rate of 8.9% on between £7,500 and £14,950. While there are slightly lower rates at the moment, this is not a bad deal. Another point worth making about linked deals such as this is that, with banks and building societies now more cautious about who they'll offer loans and credit cards to, you may stand a better chance of having an application accepted if it is with your current account provider as you already have an existing relationship with them.
Please note: Any rates or deals mentioned in this article were available at the time of writing. Products or companies underlined can be applied for directly.
Rate This Article
Click on a star to rate this article.