You don't necesarily have to have a fab credit rating to obtain a mortgage. I work for a high street bank and the criteria is based on 1.ability to pay (i.e. is there enough disposable income to cover mtg repayments) 2. deposit saved (ideally about 20% of property value, however some lenders are happy with less) 3. property valuation (is it worth what you are paying for it).
I have known us to give mortgages to people who are new to the country & so would have no 'credit rating'.
I would recommend your partner gets his head out of the sand (so to speak) & contact a credit reference agency (Experian would be good). You can get a form to do this from a local bank or online. Then you will know exactly what you are dealing with. If you are lucky some of the older/smaller amounts will have 'dropped off'! Paying off the debts would be recommended, you can also ask for a note to be put on your file which can be seen by any lenders who search on your partner. Something along the lines of 'I got into debt due to personal circumstances & extreme financial pressure but am now actively repaying money owed & wish to state that I will deal with any future borrowing responsibly'
I hope that helps & good luck.