My existing credit card won't increase my credit limit so I have decided to apply for a new one. I have heard that it can be difficult to get a new card so should I apply for 3/4 on the basis that that will increase my chances? Please advise.

Everytime you apply for a credit card, a record of each application is made on your credit file with the large credit agencies. One or two applications will probably be OK but your credit score, the calculation which determines whether the agency thinks you are credit worthy, will be damaged if you send in repeated aplications. This will lead the credit card operators to either refuse your application or reduce the level of credit they are prepared to offer.

Incidentally, it could be a good move to get a copy of your credit file from one of the credit agencies. Ask Experian, they are the largest. You'll find their details online. You will have to pay them £2.