Three silently launched 4g yesterday, so you should be able to access that (depending on where you live) soon. And it's a free upgrade, no changes to your account from what you have now. Saw a guy on the test getting 40mb down, 20 up on his phone yesterday. Sounds great for umlimited and tethering!
Depending on your location, changing provider may not have that much effect on your speeds. If there's no cable or fibre optics in your area then it'll be down BT's cables and the speed will vary with your distnce from the exchange. . .
Do you have Sky TV? Add their BB package for £7.50, no limits, no throttling. Never had a problem with them. As for mobile, I use Three's One plan 2000min, (+5000 3-to-3mins) 5000 texts, unlimited (genuinely) data, and the ability to tether. £15/m on contract, £18 without.
Sorry Peter, I thought I'd replied to you...( I'm at that age I reckon
I don't have Sky so that's out. I'll look into THREE as I still haven't sorted anything out regarding my mobile as I've been sorting out my household insurance and saved £180 on the annual premium just by approaching my existing insurer which is not bad so I'm on a bit of a roll.