If you use the telephone line, Ethel is correct, you are stuck with BT for your telephone for 1 year. After that you are free to choose other telephone companies. However, you can choose any company for your broadband and that will be a separate bill. Note that you will also be signing a 12 month contract for your broadband. You can go to a price comparison website and see which broadband company has the best price at the moment.
However, if you are lucky you might live in an area which has cable. This means you can phone, Internet and TV through a cable (which is not the BT phone line). One cable company is Virgin Media. Go to their website, put in your postcode and you will find out if you can get it. If you can I would highly recommend choosing that over BT. BT are notoriously slow at connecting your line when you move house, and they have a tendency to overestimate how much you should be paying on Direct Debit.
The third option is mobile broadband, which is - mobile! You get this from a company like Three (3). You may have noticed that shops like Curry's are offering you a free laptop if you sign up to an 18-month mobile broadband deal. You get a laptop, a USB gadget and you can use the Internet wherever you are.