There's no such thing as a 'right to credit', so lenders are free to determine how long you'll have to wait before they'll give you a card.
The most commonly quoted figure is 6 years but if you win �10 million pounds on a lottery roll-over this weekend, you might find that you could have a new card by next week ;-)
Whilst adverse credit will remain on your credit file for 6 years, that does not mean that you can't get credit.
The sooner you pay off any arrears and CCJs, the sooner you will get credit.
As a rough guide, once you have paid off all your arrears, you will probably be able to get a credit card from someone like Capital One within 6 months to a year.
Make sure that you go on voters role where ever you are living and try not to move around too much.