I use Tesco for £2.97 a month. This covers unlimited landline calls and 10p a minute to mobiles (except the 3 network which for some reason is more). There are other packages including Pay As You Go
It plugs into the router so is not dependent on the computer being on.
The non-computer option is quite expensive to set up. The wireless phone (which takes landline calls, if required, as well as internet calls) is 54 pounds and extra handsets are 34pounds. Good quality Siemens. Once set up it is very cheap and efficient, though there is a shortage of the DP450 handsets and box to plug into the router in stores.
http://www.tescointernetphone.com/
For some reason, if you want to register online it would not work for me with Firefox, only Internet Explorer