Absolutely Dave! I'm with Tesco mobile too and have always found them to have very good coverage. I have to say I'm a bit nervous about it all since I've not previously had a smartphone. I may decide not to set it up until after we get back just in case anything goes wrong. The old phone has always been OK when we are abroad and I would hate to be out of contact with the family.
You can sometimes buy a roaming package for a week or month, depending on the country you're visiting and the provider. I'm not aware of Tesco offering anything at the moment but i must admit i haven't looked too closely.
Failing getting any cheap data if you use whatsapp for messages you can utilise any free wifi available to send messages/pictures etc free of charge to other whatsapp equipped recipients. Watch out for sending "normal" text messages even by wifi abroad, the cost can be crazy ! You can also use facetime (or android equivalent) to make video or audio only phone calls, providing you have wifi (or cheap data).
Apologies if i'm teaching granny how to suck eggs here, but i only sussed all this out last year