Thanks everyone, and thanks Polter for the link.
I think we will first contact the previous buyer's surveyors, good idea thanks.
The Basic survey report has come back as expected, some evidence of old damp/woodworm etc.
However, we have also just had through all the other docs. Damp proof course and timber treatment for woodworm and rot for whole house done in 2010 and guaranteed for 30 years, at any point in those 30 years we can get a quote and get work done if necessary for free (it's a big national company which I've heard of, so seems legit). So that is nice 
It also had a survey for subsidence done in 2010 and some underpinning to the (modernish, 1970s I think) bay window, but the rest of the house was fine then. Very reassuring as we've lived in subsidence areas before.
Windows are less than 10 years old with a 10 year guarantee, also nice. (We know one velux window needs replacing, but we offered knowing that.)
I'm leaning towards contacting the old surveyors, but if nothing comes of that then I'm inclined to get some specialist surveys/quotes as at least 2 of those can be done under guarantee if anything needs doing, without the cost of the survey. Also, there's probably nothing the survey could say that would put us off completely! So if it needs work, it might even save time to start with quotes (don't worry, we'd get multiple quotes and not be conned into doing unnecessary work - if there's one thing I've learnt from Mumsnet it's how to stand up for myself and get a good deal!)
Thank you for all the advice and ideas!