I've had a DMP and been able to get a mortgage twice through a specialist mortgage provider.
I set up my DMP in 2006 and made my last payment in 2017 (finished early).
I set up a DMP as my ex ran up huge debts in joint name loans, living off credit cards in my name etc before I kicked him out. The DC were little and I only worked a few hours a week and very, very quickly the debt got out of control because my ex refused to pay anything towards them. I requested an IVA but a DMP was offered as a better solution for my circumstances.
I remortgaged with a specialist mortgage provider in 2006 to put the house in my name only and pay off my ex who was insisting on getting his share of the equity in the house and I got a joint mortgage with my new husband in 2010 (different house) with a different specialist provider.
Whether I would have been able to do any of that (DMP, remortgage, new mortgage) without already being a home owner, I don't know.
Expect to pay much higher mortgage interest rates (x3), larger mortgage provider fees (at least double), generally it will cost you a lot more than someone with "good credit".
If I could "do it all again", in hindsight I would have sold the house back in 2006 and paid off the debt in one go. I thought I was giving my DC more security but I was actually just living a miserable life, hand to mouth for years. It was an interest only remortgage so when I eventually sold the house most of the money went back to the mortgage provider and the equity went to my DMP plan. I gained nothing from the arrangement apart from a hard life lesson.
My advice to anyone in similar circumstances is please go to Step-change or a similar debt counselling service and don't try and struggle paying the debt with interest included as "it's the right thing to do". The debt will very quickly get out of control if you can only afford to pay minimum payments and you will end up paying far far more than your original debt amount.
I HATE any type of credit now, it's offered too easily and, despite best intentions, IMO you only need ONE BLIP in your plan to repay and you are fucked.