The usual wisdom is that it is unwise (in pure financial terms) to save whilst in debt, because you will pay a higher rate for your borrowing than you will ever get for your savings. Whether it is "a good idea", however, does not depend on pure financial logic alone. I choose to keep savings that I could be using to reduce my debts because it helps to have some flexibility, and if I exercise that flexibility by spending on a credit card, I mess up some good balance transfer rates... so I'd rather keep spare funds in cash.
If you have the sort of debt where you could reduce and increase it without penalty (i.e. a credit card at a single fixed rate, or an overdraft well within limits) then the financial logic applies... it is better to reduce your debt by £500 now and increase it again when the boiler breaks down (or Christmas comes) than to keep the debt at 10% interest and the savings at 1% interest.
Given that you have a DMP, I'm assuming that you can't easily get more credit to cover Christmas/the boiler breaking down/whatever, which makes a case for having savings in cash if you possibly can, even if that means that you take longer to clear the debt. Obviously, if and when you have a few thousand in savings, divert any surplus to paying the debt.
Finally, and I know this isn't the question you asked, but from experience I feel I ought to add... while I think that having savings is good, I don't think you should be saving up to buy Christmas presents/holidays/luxuries that you couldn't otherwise afford; that's what got me (and maybe you?) into debt in the first place.
I don't mean to preach (I'm still in a similar spot) but recognising that you can't afford it will let you keep your savings and get out of debt quicker. It has taken me quite long enough to realise this... save by all means, but blow it on Christmas and you're in the same rut that caused you to use credit in the first place. If you want out of debt, then get your expenditure below your income at any cost, including reducing Christmas expenses... I spent about £50 in total on Christmas and frankly don't care what people thought of it. I'm now in less debt than I was, and with more savings.
Best of luck with your savings, and may you remain frugal!