BE and o2 are same company as my speed check comes up as Be although im with o2.
the router they provide is poor and you only actually rent it and give it back at the end but sounds your like me want the speed for the gaming.
I went with their ADSL 2 package because of speeds up to 20mb. I'd check on o2 website see what speed you can get.
Then i'd buy myself a 2nd hand netgear router (i got dg834GT)and load it with custom firmware for the netgear router from the dg team (google dg team and top link). It does all the stuff netgear designed to do and more.
the best feature is lowering the SNR ratio, most providers set a minimum of 6db to keep the connection highly reliable, as they cant be doing with 10,000 calling up because thel ine cant handle a lower SNR. with the custom firmware mine reports at 6db to the exchange but is actually at 2.8db.
this has increased by internet connection from 4.7mb to 7.5mb on average.
If you do get any broadband use a cashback website. o2 give first 3 months free and £50 cashback. So at £10 a month for 20mb (if you have o2 phone) then it will cost you £40 for broadband for the year.
I use http://www.topcashback.co.uk or http://www.quidco.co.uk for the cashback