Part Buy Part Rent - with bad credit

Hi

First I would like to explain my circumstances.
Some time ago I had HP for a car with Welcome Finance and defaulted on repayments (I've returned the car half term but apparently some insurance that come with it was to be pay for full initial term - I've challenged this via solicitor and eventually Financial Ombudsman but after 5 year battle my solicitor dropped the case stating that is unable to recover despite FB ruling in my favour). Since than (about 2 months ago) I've contacted the WF and have settled the default. This has been recorded on my credit score as partially settled and no money owed. Other than this my credit record is very good.

Now, I would like to finally get my first flat in part buy part rent scheme. This will be as joint with my fiancee. She got good credit history but low income (about £13000pa). I got income of £35000pa but credit history is bad
I'm worried that we will be unable to secure a mortgage.

Is there any chance for mortgage? Should we apply with my girl as main applicant?

Any advice?