It sound OK to me if you want the house and are prepared to wait. Ensure your solicitor is keeping the money safe and correctly. The only thing I'd be looking at is whether there's clauses in the agreement to allow an out if TW goes bust or into administration, that kind of thing.
The solicitor I used for two house purchases, did go under for some nefarious reason, not when I was using him but someone I know was in the middle of completing a house with him. They couldn't complete because of it but did get their money back.
I think it's normal to be nervous though, it's a lot of money, a big liability if it did go wrong, which doesn't sound likely but just get some more advice if you need it, someone else to read the contract.