A DMP will not necessarily be noted on your credit file, unless a creditor specifically asks for a note to be added. However, what can be seen by other lenders and anyone who runs a credit check on you is that you've been making underpayments each month.
If you have any other credit issues like late or missed payments or arrears that exist alongside a DMP, these stay on your credit file for a period of six years. After this period, they can't be seen on a credit check, but a mortgage lender might ask you if you’ve ever had any. It’s always best to be honest about this, as it’ll save you time and disappointment further down the line.