The only way to improve your credit score in any meaningful way is to find a way to get some credit (credit card, loan, mortgage etc.) that you can afford to pay off and stick to it. Basically what you have to do is show the credit agencies that you can be trusted (again). This will be very difficult because your past actions have made you a bad risk so low interest credit will not be available to you and you will have to accept higher interest rates. The weighting of your CCJ towards your score will decay but it will take a longer time than other negatives would. Incurring a small balance on whatever credit card you can get accepted for (unlikely to be a good one with perks) each month and paying it off in full can help towards this but what ever kind of credit you take be careful not to let the principal, or the amortising payment in the case of longer term debt, get above what you can afford to cover at the end of the month.
A bizarre effect that many people looking for a mortgage after living their life so far entirely debt free come across is that the credit agencies only do their analyses based on your credit history so a lack of credit history can be worse than a bad one.
Finally make sure that you are on the electoral roll at your current address, that you have recurring contractual bills (council tax, phone, gas, electricity etc.) in your name at your place of residence. This is because having ties to an address makes it easier for collections companies to find you if you default on credit and so credit ratings agencies place a high rating on that as a factor. Also consider getting an account with an agency such as Experian where you can report previous addresses, accounts etc. which add to the evidence supporting you.
I understand how difficult having bad credit is and am glad that you are trying to repair it.