First off you need to grab hold of a copy of your credit file from the main credit reference Agencies: Equifax, Experian, Call Credit. Get the basic service for £2 where they send you a copy of the file - you will find it buried deep within their websites. Don't sign up for their expensive credit monitoring services - they are a waste of money. Just £2 per file is all it takes.
Once you have your files you will know why you are being rejected. It could be there is incorrect information on there - in which case you can get it removed. Every time you apply for a Bank Account, a search is done on the file. If there are a lot of searches in a very short period of time, it reduces your credit score. This makes it harder to get credit or an account opened. It does not make any difference if you are not borrowing anything, the process is still the same. The first step is knowing what state your credit files are in. Then you can do something about it.
Defaults have to be removed after 6 years. Even if you clear a debt, it still stays on the file as being defaulted but is marked satisified. Then after 6 years it is removed. If a lender has not been able to contact you about a debt or has not had correspondence or a reply from you about a debt within the 6 years, they have to cancel that debt at the six year point. However, the six years starts all over again if they get a response or communication form you about it. All this is very unfair I know.
Having defaults on your file does not mean you cannot get credit. I recently helped a client get serious credit facilities when his credit file was in a terrible state. First we corrected all incorrect data on the file. Then he got a job which paid a regular salary into his Bank account for 3 months. Then he applied for credit over a 6 month period (mobile phone month 1 etc) and made sure all bills were paid on time. After a year, he could demonstrate good payment records and was able to open a business account, obtain credit facilities and now operates a modestly successful business.
In your specific case it starts with getting a copy of your credit file. IN the short term go to any high street bank and demand they open a basic personal account - something they are obliged to do by law. Then request in writing they will offer you a proper account with facilities within 6 months providing the account is operated properly.
This should get you started. You then have 6 months to prove your case to the bank. Meantime, you can use the basic personal account for the business in the short term whilst you build up your credit status again.
Hope this helps