It is correct that you shouldn't make a lot of applications (like duplicate posts, it can be annoying). Hopefully the errors in your credit file have now been corrected.
You should consider trying to pay off the Vanquis card first and cancelling the agreement for two reasons. This card has a high interest and the fact that you have one of these cards (they are marketed at people with credit issues) will be recorded in the credit file.
You do need to appreciate that most lenders will do the same calculation as you and decide that you've already borrowed enough. It may be that you need to deal with your current debts before borrowing again.
If you are struggling, it may be worthwhile to have a chat with a debt adviser at your local Citizens Advice Bureau.