Tesco mobile piggybacks off the O2 network, so will work anywhere that has O2 coverage. I'm sure most branches of Tesco now sell SIM cards for all the main networks, as well as their own Tesco mobile service.
4 main networks in the UK - EE, Vodafone, O2 & Three (3), with various others selling services that piggyback off them. Unless you are going somewhere particularly remote, or are unlucky, any of the networks will provide decent connectivity.