Hi
Unfortunately defaults and CCJ's will stay on your file for six years, although according to the credit reference agencies they do diminish slightly in significance as time goes by. However it remains unlikely that a mainstream lender e.g. most high street banks, will give you a credit card. Your best option would be to apply for a card with either Vanquis or Aqua who offer cards to those with previous credit problems. The interest rate is penal, but if you pay it off in full each month you will not incur any costs.
I would also suggest holding off future applications for a few months as too many applications within a short period of time may make it look like you are desperate for credit.
Hope this is useful.