Definitely do it - it's one of the few things that isn't considered Deprivation of Assets.
My mother (in her early, undiagnosed phase) bought herself one, completely forgetting she'd taken one out years ago that she was still paying monthly. Fortunately, the old plan was for a cash payout and the second one paid all her actual funeral costs so we were able to get both...
A couple of things: beware taking out one of these plans (and the 'over 50s savings plans') because if you live long enough, you will pay in more than you get back. This was the case with mum's cash plan and she knew how useless it was because she told me about it. The trouble is, unless you keep on paying the premiums every month, you won't get the payout. Fortunately, mum had had the plan a long time so it was only about £3 per month but even so, it is galling to keep paying something when you know the amount you'll get back is fixed.
Second thing: the plan mum took out (for the funeral) was with Golden Charter (other companies are available) and related to a funeral director in the area she lived. But I moved her to a care home near me so I was a bit concerned. I contacted the company and they said it was no problem as it was all transferable to a local FD. (I think I was given a choice of a few local ones that were in their scheme and one was the nearest to me that I would have chosen anyway.) The transfer was done quickly and easily so my advice would be to make sure the plan can be transfered in case the person needs to move at some point.
When mum died, I was really grateful that she had the plan as the FDs did everything - I just had to make one phone call to them. It made the whole 'dealing with death and organising a funeral' thing so much easier. I'm going to make my will, set up LPA, etc, as soon as I've completed my house purchase and I will definitely be buying a funeral plan too.