As the others have said, it varies massively depending on where you live, so the best bet is check out the online coverage maps and then get PAYG sims to check the signal for each network (EE, Three, Vodafone, O2- the others such as BT Mobile or Giff Gaff use the networks of those four).
In terms of coverage and performance:
EE- The best overall as they have a good 2G network for calls and texts and, while slow, usually you can get usable data over 2G to at least send an email or a Facebook message over EDGE. Their 3G is very good and they have the best 4G coverage with much of it double speed 4G and even 4G+, meaning lots of capacity and fast speed. I intend to move to EE when my contract runs out in the next couple of months.
Three- 3G coverage is more or less as good as EE's. Occasionally you can get 3G on Three and not on EE or vice versa, but it's rare from what I'm told- they are basically the same. However, they have no 2G coverage so if you want to call a lot you may find yourself without a signal in some places when other networks have a signal. This is thanks to the poorer coverage of 3G compared to 2G. Three are great for data though, although their 4G coverage isn't a patch on EE's. I'm with Three now and I am impressed with their network as a whole. It's just the lack of a 2G backup and poor 4G coverage that lets them down.
Vodafone- Good 2G coverage so great for calls and texts- maybe better than EE in places thanks to the use of a lower frequency (900 Mhz vs 1800 Mhz). In cities they have good 3G and 4G coverage, but they haven't invested in these technologies as much so, although things are improving, there are areas where Vodafone users are on 2G only and those on EE can get 3G or even 4G. They do have a good amount of 4G spectrum though so will probably be close to EE performance wise once all of their masts are upgraded.
O2- Just as with Vodafone, good 2G coverage thanks to lower frequency used but poorer 3G and 4G coverage and performance. Less 4G spectrum than Vodafone so lower capacity and speeds on 4G.
Overall, EE is the best, but I have heard of places where the data speeds are less than 1 Mbps on EE and Three and 20-30 Mbps on O2 and Vodafone thanks to a 4G mast being nearby from those operators, so EE aren't always the best performing network. Likewise, people say EE aren't as good for calls but Rootmetrics has them as the best for call performance and my parents struggle to get a signal for voice on O2 at my grandparents yet EE seem fine.