Thank you all, I'm now quite sure it's a fake, but to answer the questions: -
It's not magnetic.
The groove width varies slightly around the circumference on both sides, and in places on the obverse the beading (?) is missing.
I suspect that, yes, it would have originally been painted, but that somebody cleaned it off, or it simply wore off, before it came into my hands.
I have a small collection of 50p £1 and £2 coins which I have kept when I've found them in my change, so I'll keep this one with them. My wife threatens to do as John Peel's wife apparently did and put them towards my funeral, so I'll make sure to clearly label it as a fake.
I have what appears to be a 1998 two pound coin, in very poor circulated condition. I'm pretty sure it's a fake.
It was among the effects of somebody who recently died.
For a start, it's mono-metallic, and there is a lack of detail in the Queen's portrait: -
It weighs 13.2g
At first I thought it was silver, it was well oxidised when I found it, and it cleaned up well with silver polish but I can't find anything that was minted that matches. Whatever the metal is, it's very soft.
I'm beginning to think it's simply a fake. What do you think?