Hi Kittylette.
The fact that you have store cards and a catalogue account means you have a credit history, however small, so I find it unusual that you are struggling to obtain credit if you have not had late payments,defaults or CCJ's. I recommend you get a copy of your credit report to make sure there is nothing on there you are unaware of.
Some lenders will not lend for home improvements unless you actually own the property, crazy I know but it may be one of the reasons you are struggling, or ytou could be applying to a prime lender, offering the best rates, but where it can be difficult obtaining credit unless you fit their criteria perfectly.
One option available to you is to use a broker, they tend to cater for the whole of market, ranging from prime to sub prime. The APR offered may be high but it is likely they should be able to help. Try UCC (The Unsecured Credit Company), you can apply via moneysupermarket.com.