Of course they do, and be aware of the HMRC automatically assuming you get the annual increases to your DWP pension and hence a reduction to your other pensions tax free amount. This happened to my father to the tune of over 900GBP before he spoke to me about it.
In my case I have 2 private pensions, a small annual one which is a fixed amount and a larger monthly pension which has annual increases. They set my tax code based on the monthly getting no increases and gave the small one all the remaining allowance. OK for year 1, but year 2 tax was deducted despite the total income being 5,000GBP less than the personal allowance.
In neither case was there any problem getting a refund, I just wrote to them explaining the correct situation, they were quite quick to reply.