I can't think of any other ways to leave the UK than by boat, train, and aeroplane, and I've been checked at all of them.
UKBF checks passports on departure at the Eurostar. At manchester airport at least, there are no routine outbound passport checks by UKBF
On travelling to the continent by boat (hook of holland) checks at the far end. Eurostar checks at re near end. Flying checks at the far end.
I assume that Americans get exit stamps at the first check. Most countries that stamp passports give entry and exit stamps, whether you have a visa or not. More and more counties rely on computers to keep track of you though - Israel used to stamp you at Tel Aviv, now you get a piece of paper that you return on exit (you still et stamped at Erez when going in/out of Gaza). In 2015 Australia stamped when you use the manual system, but not the automatic system. I don't recall if the US stamped my passport last time on the way in, I don't think Canada did. Hong Kong stopped in 2013 I think.
It's a shame, I like stamps. Plenty of them at Lagos last month though - 2 stamps on the way in, 2 on the way out, as well as the full page visa.