Thank you everyone for your feedback!
I've now been to see him with my mother. Other than this sudden accusation his mental faculties seem completely fine. He's a very sharp gentleman, and his short and long term memory are probably better than mine are. He knew when we got there that we were going to try to get him to see a doctor, and kept telling us he was healthy for his age, and the same as always. He thinks the problem is that he is lonely and feels depressed. He lives alone, and his brother passed away not very long ago. He doesn't have any children. This did come up as a common cause of paranoia in the elderly in my Google searches, but I'd rather he saw a doctor to get checked out than to assume this. He made it clear he wasn't doing that.
For now we are going to shelve trying to get him to see his GP, as we don't think he is at immediate risk if it is a health issue or that we'll be able to convince him to go in the short term, and we are going to try making sure he has more company.
What was most troubling was that this was so sudden and there was no lead up to it. My experience of Demetia and Altzheimers in other relatives was there was a slow decline and confusion/memory issues before they got more agitated or distressed and began making things up to explain their changed perceptions or gaps in their understanding, but apparently paranoia can be an early warning sign of these conditions.
The accusation against my mother doesn't seem connected to anything in the past or present. She took him out for dinner with her partner, which she paid for, and then they saw him onto the train home. Nothing about this is new or unusual, she's been taking him out for meals regularly since I was a little girl, before that my grandmother was doing it, and now my partner and I go out with him, as well. He thought that she wanted to push him down the station steps. This was a week or so ago, he made the accusation on Saturday, my mother spoke to him twice between this and the meal and she said he didn't give any indication he thought she had been plotting his death! Money wise, I have no idea how much money he has, but he isn't exactly wealthy. He lives in a little bungalow, which is so old fashioned entering it is like taking a trip back in time. It seems exactly as it was when my grandmother used to walk me round after school to visit, save a few extra photographs as there have been new additions to the family. Certainly, none of us have ever expressed any interest in his money, or his will. If anything, when we take him out we have to argue with him so he will let us pay for things.