Yes.

I have always done so for the last 4 years with no problem at all.
I always cut the main thick stalk into very small pieces although I'm not sure this is necessary. Perhaps someone will say whether doing this is a good idea.

Cutting them into small pieces is alright but not strictly neccessary, all you need to do is mash them up a bit which lets the microbes get in to do their work easier, if by any chance you have a garden roller, {which is a rarity these days}just roll it over them to damage the stems, Derek.

So long as they did not have blight... Though ours go to the Council composting set up o be sure.

Blight in any case does not survive unless on living tissue and this is not likely with pieces of tomato stem or leaves, though it DOES happen with old potato tubers. In many cases blight is spread to tomatoes from potato 'volunteers' which have come up in the garden from previously blighted potato plants.
The fungus itself, Phytophthora infestans, is killed by cold weather so in a typical British winter will be destroyed.

Thanks Derekm, I'll do it as you say next year. It'll take a lot less time. And - I have had a roller for many years which has never been used !

Hi hank, glad I mentioned the roller bit then, lol, not many of those about these days, Derek.