I'm a former BT employee so I'll give a brief description of the 3 main ways companies are competing.
1st Cable (Virgin)
Nothing here is owned by BT. It's a totally independent company that has fibre optic cables that you can get telephone, broadband and TV services from. Around 45% of the country can get cable services. Check here for the latest deals and to see if you are in a cabled area :-
Simply Broadband - Broadband Size: M
2nd LLU (Local Loop Unbundled) The basics of this is you have the same line, but in the exchange they unbundle from BT equipment and plug into their own. Your new company can unbundle for phone line and broadband or just broadband, BT still makes a few quid on this, as they charge your new company for repairs to the line. Last years figures were 70% of people can get an LLU, I'd expect that to be higher now. Check what companies are available here :-
Samknows Broadband - Availability checker
3rd CPS (carrier pre select) here you pay your BT line rental but your calls go through a separate company. 100% of people with a BT line can get this.
Talktalk and Tiscali are probably the biggest LLU's at the moment, there are a lot of CPS's, The biggest are probably sky and AOL (Although both can set you up as a LLU... make sure you talk to someone that knows what they are doing if you want this option!) Biggest single piece of advice I can give you right now on this is if you contact a company with the intention of becoming an LLU customer is that if you later want to change it gets tricky as they only move ya from BT... I'm with talktalk and cannot move to tiscali as their deal is slightly cheaper... for me to do this I'd have to re-connect to BT (and get locked into a minimum term of 12 months, or pay a cancelation fee of either the remainder of my contract or £70.00 whatever is smallest) so pick carefully!
Basics to landlines. 
