Sky Broadband is only £.75 per month if you already have Sky TV. Further, that's only for the first 12 months; it's £7.50 per month thereafter.
Rather oddly, if you've
not got Sky TV their broadband service is actually free (instead of £3.75 per month) for the first 12 months (and, again, £7.50 per month thereafter).
However you need to remember that you also have to pay Sky for your line rental (at £16.40 per month). It's an ADSL service (not using fibre cables) which is fine as long as:
(a) you live reasonably close to a telephone exhange ; and
(b) you don't live in a house where lots of people will be using the internet (e.g. via a Now TV box or similar, as well as via PCs, tablets, etc) all at the same time.
http://www.sky.com/shop/broadband-talk/broadband-unlimited/
As Google denies any knowledge of a service called 'BI Broadband', I'll assume that you're referring to BT's service. They charge £4.50 per month (+ £16.99 line rental) for a 12 month contract [but give no indication of whether they'll honour that figure thereafter] but you get BT Sport for free as well. However, unlike Sky, their service is capped at 10Gb per month:
http://www.productsandservices.bt.com/products/options/new-customer.html
Depending upon whether or not you want your phone calls bundled in with your broadband package, it might be better to consider BT's budget division, Plusnet:
https://www.plus.net/home-broadband/
However you get what you pay for with all such services. To get really reliable broadband you need to be paying around £20 per month (on top of your line rental), with companies such as Claranet (which I use), Zen or Eclipse. They serve big businesses (who demand zero downtime) and provide the same quality of service to domestic users.