Any currency exchange place at Heathrow will take your GBP coins and turn them into dollars. However, you'll get a better rate of exchange downtown than at the airport. You'll find some Post Offices and Marks & Spencer branches offer currency exchange services:
http://www.moneysavingexpert.com/new...ency-providers
I don't think UK currency exchange shops will accept your Euro coins (but perhaps someone knows a place that does?). Your best bet is to spend them in a Eurozone country. Failing that, you might be able to strike an informal deal with someone who's going to the continent or Ireland.
It might be a hard habit to learn, but those coins really have value, so it's a good idea to use them as you receive them rather than allowing them to accumulate until you're a penny millionaire.