Essentially, all the networks have outstanding coverage throughout most of the country. O2s network probably goes a bit further into the boonies, but Voda and Orange probably have more capacity and better signal strength in populated regions. T-mobile's coverage is somewhat less good than the others, with a few patches in populated areas (e.g. small valleys). 3 have a relatively immature network of their own, but 3 phones will fall back onto O2's network is 3 can't take the call.
However, capacity isn't really a problem - I've never had a 'network busy' signal in the last 5 years - even at peak times. Similarly, except in the centre of huge buildings (e.g. hospitals) I've always got a signal in a populated area (Orange and Voda).
Within London itself, apart from the building problem, holes in coverage are pretty much unheard of for all 5 networks. Indeed, within the whole South East of the country, there are no significantly sized holes.
If you have an unlocked GSM phone then you should be able to just drop in a UK pay-as-you-go SIM card. (If you have a US GSM phone: Dual band will be fine for Voda and O2, but you'll *need* tri band for T-mob and Orange, and for optimal O2 performance). NB. Three SIM cards are not GSM compatible, and require a 3G (UMTS) phone.
However, a UK model phone and pay-as-you-go SIM can be bought brand new for under £40 so it's hardly worth bringing your own phone unless it's particularly good.
In terms of call costs:
Incoming calls are always free of charge to the recipient (unless you subscribe to premium content services, like ring tones, etc - where it's common for them to send collect charged material at regular intervals. Avoid these services at all costs)
There's very little difference between prices of different networks. In practice there are 2 main pricing schemes (peak/off-peak and flat rate). Not all networks offer both, and there are some minor differences between networks. Most networks will offer a discounted call cost with the larger increment top-ups.
Flat rate is around 20p/min to landlines and other phones on the home network, 40p/min to mobiles on a different network
Peak/off peak is around 30p/min during the day, and 5p/min during evening (1900-0700) and weekends.
Beware of 'non-geographic' area codes (often called lo-call, local rate, etc.) these are numbers that begin 07, 08 or 09. These are frequently used by call centres, and big companies. Calling these numbers from a mobile will usually encounter a big surcharge (including toll-free (0800) numbers).
Don't even think about calling international numbers from a PAYG mobile. There are calling cards that can be used to call international, but it's now common practice for the mobile networks to block popular calling cards. International calls are best done from a landline.