Giffgaff is the best mobile internet provider in the UK. It's not even a contest, every other provider sucks balls compared to giffgaff. With giffgaff you get unlimited internet access for 10 pounds per month on your mobile phone, which comes in extremely handy if your estate agent 'misunderstood' your inquiry about whether there will be internet available in your new apartment when you are just moving in.
The speed is excellent, but giffgaff does touch the content before sending it to you. They block adult content by default (oh no!) and the option on their website to enable it doesn't seem to work (as of writing this post). They also recompress images massively and insert javascript into each http request, adding keyboard shortcuts so you can download the uncompressed versions of images. This kind of practice is something I'm very unhappy with, but I do understand why it's necessary. Considering their low prices there's probably a lot of people abusing their network. Or O2's network rather, since that's what they're running on.
For more info check out the giffgaff.com website, and when you're ready to register, click here to give me a referral bonus which is equivalent to 15 days free internet. :)