commercial banks will only exchange them for account holders.
Depending on where you are located in the US, you may or may not have a local big bank that also does business in the UK, and they may serve you in the UK with a foreign account if you flash their debit card. Santander is one of them. I believe HSBC is another one.
As for Euro coins, look for places that have self checkouts. If they take cash, self checkouts typically won't balk at the number of coins you put into them.