would the Vanquis credit card add anything extra to these to help improve my credit score quicker or not?
No. In my opinion, as you will be recorded as using a card that is marketed specifically at people who are not good with money, it could actually put some lenders off.
I would disagree with this. The lenders will look at the ability to control the credit that is used and not who that credit is with. I would agree if the TYPE of credit was typically that used by people with bad credit such as Pay Day Loans, lenders do not like clients that rely on this type of lending but a credit card is used by all levels of credit score and it is the control of that credit - repaying the outstanding balance IN FULL ervery month that the lenders will take note of and if you can manage to repay the balance in full every month then your score will improve dramatically.
The reason your credit score is still so low is that you have the "arrangements to pay" still in place. The fact that you still have a debt arrangement will leave most lenders cold no matter when your defaults expire.
My personal opinion would be to use the 10% deposit that you have in place already and clear the debts in full. The money you were then using to clear the debts then goes to create a new deposit which can then earn you interest instead of the debt drawing more lenders interest. Take out the credit card for just 6 months, put your petrol or some other low cost monthly need and then at the end of the month make sure you CLEAR THE BALANCE IN FULL.
The fact that you no longer have the Arrangement to Pay weill mean that your credit score can improve and will do quite quickly (not over night). The correct use of the credit card will boost your credit score. Make sure both of you are on the electoral roll for your current address - The link below will take you to a page that will search for your local authorityif you need to reapply
Once your credit score has improved then switch your Vanquis card to a more mainstream (lower rate) card. Hopefully within a year your score will have improved sufficiently to apply for a mortgage and you may have enough deposit for the house you want.....and the 6 years deadline will have passed and the defaults have left your credit score