It does not sound like a good idea to me, even if you could get accepted (car dealers' "in house" schemes are probably more likely to accept you than other schemes). Leasing only works in your favour if you can be absolutely certain that you can make each and every payment. If your circumstances change in such a way that you cannot finish the agreement, you could end up with no car and a large debt.
It would not surprise me if there are leasing schemes marketed specially at people with bad credit. Such schemes will be expensive and will be designed so that the finance company makes lots of money out of you whatever happens.
We are very fortunate in the UK that it is possible to buy a decent car for a few hundred pounds. My opinion is that you should stop looking at leasing schemes and start looking at sites that will tell you how to inspect a car. www.autotrader.co.uk is also worth a browse.
If you really want to build up a good credit rating, you should not consider anything that has the possibility of stretching you financially.