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.
In banks' terms a credit rating puts you into a risk bucket whereby the less creditworthy you are seen to be the worse the bucket you are in. By improving your credit score you are looking to change bucket (seriously, that is the vernacular). The higher the risk you are, the more money they want for taking that risk and the lower the amount of credit they will be willing to extend (i.e. money they are willing to risk on you). In the past you have shown yourself to be a high risk which goes a long side a lower amount and a higher interest rate. They need you to prove that you have changed and are a lower risk but you can't do that without taking some credit and proving that you can be trusted to repay it. The flip side of this is that you need to get credit to prove that you can be trusted to pay it back. Since banks make money by taking the risk and reaping the interest rate it is almost certain that there is a bank out there who will, under conditions, extend you credit. Unfortunately the cost will be high. You need to find a source of credit that you can use but that you will not be unable to consistently repay even if you lose your job, arms, legs etc., use it and rebuild trust.
Would you lend you money?
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.
source: I worked for a retail banking credit risk consultancy