When I was looking at (and went down) this route, EE offered the highest monthly allowance at 200GB for £60/month. There may be better deals out there now with larger monthly allowances, you'll need to look. My speeds went from 6.5Mbps down and 0.7Mbps up with BT to 65Mbps down and 40Mbps up.
If you do go down this route look at the relevant forums for issues. With EE I had to select within the supplied router to use just IPv4 rather than the default IPv4 & IPv6 in order to access certain websites and to get a couple of iPhone apps to work. The other thing to note with EE is that if you have Philips Hue (as I do) then you will not be able to control the lights when away from home.