Nearly every single lender will require a minimum of 2 years accounts for self employed and more often than not they will require each years income covered by an SA302 too, this is an HMRC issued document that shows the the income declared and the tax paid. It is this income that the lenders will base their affordability against and rule of thumb is that you will be allowed to borrow around 4x your net profit (earnings before tax) for your mortgage. There are a couple of lenders that will accept 1 year but it is unlikely that you would be accepted with adverse credit
The adverse credit will not do you any favours either and may count you out of a mortgage altogether depending on when it happened, the level of the adverse and for what value the adverse is for. If you have had a default or a CCJ in the last year or 2 years then there is a high chance you will just be declined automatically, if it was 3-4 years ago you could be accepted if you have had no further missed or late payments in the last 2 years, if it was 5-6 years ago then the lenders do tend to ignore but if the debt still hasn't been repaid then this will reduce your chances again. If your adverse credit is from beyond 6 years ago then it will no longer show on your credit file. There are lenders out there that will be able to help you if you have adverse credit but you may well find the interest rate is very high to access these lenders and the fees may also be excessive. Speak to a mortgage broker and he can best advise you on who to approach.
What will improve your chance of a mortgage is the amount of deposit you can place down before you take the mortgage on. If it is only 10% or 20% of the purchase price then lenders will still see this as a high risk application and the chances of being accepted with adverse credit will drop through the floor. If you can give 25% plus then the lenders will view it as low risk and then the chances of them being more lenient with adverse credit improves.
You will not be able to buy a rental propperty until you are a mortgage holder, no BTL lenders will allow a first time buyer as a landlord anymore and the chances of you gaining a rental mortgage (buy to let) when you have any kind of adverse credit against you is slim.
The minimum deposit for a buy to let mortgage is 25% of the purchase price.
Good Luck