O2 have recently been rated the worst mobile network according to Rootmetrics and EE the best:
http://www.rootmetrics.com/en-GB/content/mobile-network-performance-in-the-uk
I'm on EE having moved from Three a couple of weeks ago and I have to agree. I did four speed tests yesterday on 4G, all in different locations, and with a full signal, I got a 66-68 Mbps down and around 23 Mbps up. On Three, only one of the four locations would have had 4G, although both Three and EE have a very good 3G network so if you end up somewhere with no 4G signal, a 3G signal normally works well too.
Of the four places I tested near where I live, two locations don't even have 3G on both O2 and Vodafone, never mind 4G, so you'll be looking at 2G only which is useless for data. They have good 4G coverage in cities and they are improving (my parents are on O2 and have been recently text informing them that 4G will come to our area soon. It is already available at the other side of Retford but it isn't yet on the mast serving this side of the town, and Vodafone mast share with O2 now so they are set to get 4G here too), but they really lag behind in some areas of the country, the south west being an area that is particularly bad on those networks.
Don't get me wrong, EE has some not spots too. There's a place not too far away with 4G on O2 and Vodafone and only 3G on EE and Three. There's also places that have a week EE and Three signal yet O2 and Voda have a strong 4G signal. Overall though, EE have the best 4G coverage, and the deployment of 4G on the 800 Mhz band will solve their biggest weakness- indoor coverage*- very soon if you have a handset purchased direct from them that supports VoLTE (4G calling).
If you are thinking of changing networks, always check their coverage maps first. Once you have done that, I would recommend getting a sims from each network and checking signal strengths, and maybe even putting a bit of credit on them and check the data speeds. I say this as I get quite a weak signal when in my room, but turning WiFi off reveals it's a weak 4G signal, and a speed test gives results of between 30 and 40 Mbps download speed normally. You should also check anywhere else that you visit a lot (such as where you work/study etc) before changing networks.
Feel free to ask for more information if you want. I'm studying Electrical and Electronic Engineering at uni and, although we've not had any lectures on communications yet, I'm very interested in it and have been learning about how it all works. It's why I've not been on here much lately, that and the fact I've been out and about with the family a lot over summer!
*Their indoor signal can be very good, but they use higher frequencies than Vodafone and O2 so the signal doesn't travel as far and can't penetrate through the walls of buildings as well, so Vodafone and O2's 2G and 4G (and 3G where they have deployed it on 900 Mhz) will travel a little further than EE's. Don't let that put you off though as there are loads of factors that could effect things.
--- old post above --- --- new post below ---
Just to add, here are the different data icons you will see on your phone:
G- GPRS, a 2G technology. 50 Kbps speed so very slow.
E- EDGE, a 2G technology, 220 Kbps speed so still slow.
3G- Obviously 3G, you won't see this icon often now unless you have an iPhone as it represents the original 3G standard with speeds of about 300 Kbps.
H- HSPDA, a 3G technolgy with speeds up to 14.4 Mbps. Older masts may have speeds of 7.2 Mbps but I don't think many exist now that are this slow.
H+ -HSPDA+, a 3G technology, max speeds of 21 Mbps. Shown as 3G on an iPhone
H+- DC-HSPDA, a 3G technology, phones don't show the difference but this uses two carriers to boost speeds to a maximum of 42 Mbps. Many 3G masts are now using this technology. Shown as 3G on an iPhone
4G- As you might have guessed, this is 4G and will give the fastest speeds.
4G+- Not all phones and networks show this, but this indicated LTE-A or Carrier Aggregation, where carriers and even different frequencies are used together to boost speeds. Sometimes shown as just 4G.
I hope you have found that useful and I haven't gone into too much detail!