You will fnd them in larger supermarkets in the UK - there's a Coinstar in my local Sainsbury's in London (yes, same brand!)

In fact, here's the UK website, where you can seacrh for machines. Can't help with the 'continent' I'm afraid:

http://www.coinstar.co.uk/uk/html/a-home

Never seen a Coinstar machine in France. But we have a lot of beggars in Paris who generally accept even the small coins.

I use my extra Euros (except for ~40-50 in bills saved up for my next trip) to pay down my hotel bill before charging the balance to my credit card. This way I never have a bag of coins coming home with me.

Whatever coins I have smaller than 1 euro I put in the unicef collection bag on the airplane coming back to us.

Thank you, Kate! That takes care of the GBP for me, perfect!

If you have British coins going back many years, you'll find some of them have been replaced and are virtually worthless. The last coin to be replaced was a large 50p coin in 1997, and I doubt even banks accept them now. The only coins that haven't been changed since decimalisation in 1971 are 1p and 2p, 1/2p was abolished in 1984. Large 10p coin (same size as old 2 shillings) and large 5p coin (same as old shilling) have been replaced with much smaller ones in early 90s. So before you bring over your bag of British coins (and they do weigh a fair bit), check with http://www.24carat.co.uk/photogalleryofcurrentbritishcoinageframe.html.
As for continental coins, remember many countries changed over to euro in 2002 and former national coinage is either no longer exchangeable (e.g. France) or only at their central bank within varying time scale. Euro coins are of course freely accepted throughout Eurozone.

Thanks--no, they're not going back many years, I only visited Europe/UK for the first time a few years ago (and have been visiting several times a year ever since!)