Travelling with our AT&T-based iPhone5s

In a few weeks we go on a cruise vacation. We fly from the USA to
London and spend a couple of days in London (hopefully sleeping off the
jet lag), then on to an 11-day cruise around the British Isles (Ireland
and Scotland, no Wales), followed immediately by a flight back to the
USA.

We'd like to be able to maintain contact with our adult children for
emergency purposes. We have no experience using telephones overseas.

Can someone either make suggestions, or point to some good article that
contains suggestions for using your phone in that manner? We'd like to
avoid, if possible, astronomical charges for that previlege, but don't
have the foggiest notion what to do or what to not do.

Thanks in advance for any advice you can offer, or point us to.