EE is probably the best, followed by Three. Three has the benefit of unlimited data tariffs, and 4G is rolling out, and its entire network is 3G and most of that supporting the fastest version (DC-HSDPA) for speeds of up to 43 Megabits (realistically, 30Mbps is the fastest you'll get).
EE however has more 4G and the benefit of 2G in rural areas, although that's slow and almost certainly not usable for streaming anything.
O2 has some really old legacy sites that have incredibly slow backhaul connections, so for streaming - forget it. Vodafone is much the same. Even near big towns, you can find that yourself with 3G but speeds of 0.04Mbps or worse. No good for streaming, and there's very high latency too.
Fine for voice, SMS and perhaps some basic email but I don't have much good to say about O2 or Vodafone, two networks that seemed content to do the bare minimum for rolling out 3G and increasing speeds when it had business customers happy to pay anyway.
Where there's 4G on O2 and Vodafone, it's great (and at the same time, capacity will have been increased so 3G will be better too) but that's not going to be much use on the rail network for some time.
Orange still has some legacy sites not yet brought into the EE/MBNL network, which are also incredibly slow. But they'll all be upgraded before the end of the year.
Hope this gives some background.
As a quick summary: For the best coverage for voice and data; EE - but expect to pay a lot for data, which will be used quickly for streaming.
For the best value and the next best coverage, as well as very good speeds most of the time, it's Three. Get the One Plan for £20 a month (12 month SIM only) and you'll get unlimited data, 3G and 4G, plus tethering so you can share your connection with a laptop, tablet and computer - even a wireless enabled TV or set top box!
Other notes; EE has by far the most spectrum, so will have the best data speeds - and can offer double speed, and soon LTE-Advanced (aka Cat 6) which offers speeds of up to 300Mbps! But they charge more for double speed and goodness knows what they'll charge for LTE-A!
O2 has the least spectrum, and got a 4G licence cheap on the understanding it would roll out coverage to rural areas the quickest. It will do so at 800MHz, which provides excellent coverage but slower speeds. It's a trade off, but one that is acceptable as it will give coverage to people who may have no 3G or 4G coverage otherwise.
Vodafone and O2 use 800MHz, while EE will use 800MHz later this year or next. Three will also use 800MHz for 4G for rural areas and city centres, which will make a big difference to coverage. Lower frequencies penetrate buildings better as a general rule.
EE also has 2600MHz, which will be great for congested areas and provide even more impressive speeds - in theory... but that's some way off.
Oh, and on a recent trip from York to London, we managed to stream YouTube videos of trains, including episodes of Chuggington on iPlayer, for my son without any major hangups at all. That was the ECML, which bar a number of tunnels near King's Cross is pretty well covered all the way (and this was on Three). I expect good buffering covered for the odd drop out, but it never stopped the video.
