i understand that you are concerned about your house if you go bankrupt but as there is little to no equity in it there is very little risk to your home. The official receiver would take your title deed and look at any beneficial you have in the house not your partners. if there is no to little equity you would have the option of buying back your beneficial share from the OR for a nominal fee of around £1000. If you did this then there would be no risk to your house in the future if there was a substantial equity increase.
If you did not buy back your beneficial share then the OR has up to 3 years from the start of your bankruptcy to see if there is a rise in the equity, if there is then they would simply put a charge on your home for this amount for when you sell in the future and if there is no rise then the title deed passes back to you with no further future action.
I did a quick calculation based on the information you have provided and it will take you roughly 10 years to pay off your DMP. If you went bankrupt and could afford to pay towards your debts you would be debt free within 3 years.
I would advise getting a quick sale valuation from a few estate agents to see the average equity amount and if there is less than 5k then the OR will be highly unlikely to look to release this as it would cost as much to enforce this and sell the house.
I have attached a link to an article I think you will find helpful. Stay in touch and ask if there is anything you need help with.
bankruptcy and my house
Melissa McDonald writes articles and blogs about debt solutions and how they can be implemented. She aims to reassure people having debt problems that they can be debt free!