I would say the major difference between TT and Virgin's Broadband is the fact that Virgin will give you a 10mb connection straight away whereas TT will give something between 1 and 5mb (dependent on your distance from the exchange) some 6 weeks after you move in.
If speed isn't an issue, and you don't mind waiting then TT will be a lot cheaper than Virgin (assuming you keep your current deal).
Have a look at
this for Virgins package deals. If you only want BB and telephone then it looks like £14 a month initially which goes up to £25 after 3 moths.