I think your best bet is to be patient and save for the next couple of years while you wait for the 'problems' on your credit records to come off...
It isn't straight-forward or cheap to do a Buy to Let (BTL), and your step-dad would have to want to do you a BIG favour...
Firstly, there are big fees attached to starting up a BTL - around £2-3K, possibly more (depending on circumstances). Do you have this amount saved up, or are you hoping your step-dad would pay the fees for you?
Secondly, there is a maximum 75% loan-to-value on BTL mortgages. The buyer has to contribute at least 25%, and more often 30-35%. This means that if a house is valued at, say £100K, the maximum loan available is £75K. So your step-dad would need a big chunk of capital available.
Thirdly, interest rates are higher on BTLs and there are fewer good 'deals' around. A buyer should expect to be paying 6%+ interest.
Fourthly, mortgage companies insist that the predicted rental income is at least 125% of the mortgage payments. It would not be possible for your step-dad to charge you a low rent that only just covered the mortgage, unless he was making up the shortfall himself.
Fifthly, only mortgage interest is tax deductible on a BTL. If your step-dad took out a repayment mortgage - which you is definitely what you will want if you want to own the house in the end - then he will have to charge enough rent to cover the repayments too, but he will also have to pay tax on the repayment amount. This is not just an extra cost, but also extra admin for him with the Inland Revenue.
Sixthly, as a landlord he would have legal liabilities. Not just your contract rights, but also to maintain and check all gas and electrical appliances, do fire checks, have buildings insurance, etc...
Lastly (I think!), houses have maintenance costs. If the roof falls in or the boiler needs replacing, as your landlord, your step-dad would be legally liable to replace these... He will know that, since he already has other rental properties - and it may explain why he's not keen. The bottom line with 'normal' BTLs is that if they become un-economical, then landlords can sell the house... But you want to keep the house, so you are asking him to carry a lot of ongoing risk.
I'm taking out a BTL myself, because I can't tell my house and it's the only way I can move right now... But I'm pretty certain I wouldn't do it for anyone else!