I find when I'm traveling outside the US, in general, it's easiest to carry a small amount of cash for small purchases and for tipping (although not as common in Ireland and the UK). It also comes in handy for the different kiosks in Europe that don't take US chip & signature credit cards.

All the above advice about using ATM's, especially bank ATM's, is solid. I'd suggest carrying 50 euros in Ireland for 2 days, and probably around 100 pounds in London. Also make sure your credit card doesn't have a foreign transaction fee.