UK seems to be very similar to the US in that regard. A large airport typically handles the whole airspace in its vicinity. In the US, the indispensable ForeFlight gives you the right frequencies for any given place on the map. That is very useful. However, it also means a lot of frequency changes and often difficulties with coordination. It is quite typical in the US to have to request the same service over and over when switching between sectors and get different service levels. I don't have much experience in the UK but it appears to be similar.
Other countries like Germany are a bit different. Here, the airports only perform ATC for their control zone, typically not more than 3000ft AGL and a few NM around the airport. Everything else is handled centrally in tree FIRs in Germany (Langen, Munich, Bremen). FIS is also provided by those units. A few exceptions exist, typically around airforce bases where the military performs ATC.