Beware, though, that if you're not in a local loop unbundled area you'll still need a BT engineer to visit the exchange (unless you already have a dial tone, but in that case you wouldn't need one from BT either - so as the previous owners had the line connected this is odd!). So the wait may be the same.
I wouldn't choose a different supplier over a 2 week wait; I'd choose the cheapest or the one you're happy with depending on your preference. Some of the LLU suppliers are atrocious in terms of customer service.
By the way the £120 fee only applies to BT if an engineer has to go out, and it's waived if you take BT Broadband.