Think it depends on what kind of survey they are doing. When I sold my last house the person buying had the basic survey and the surveyor was there for 6 minutes in total - just looked to make sure the house was standing up basically! Didn't check under or behind anything.
If you have a more detailed survey they do a lot more, checking electrics, damp, roof, etc
Look at structure of building commenting ion materials, age and condition, comment on any extensions and maintenance issues, assess its valuation for mortgage purposes and a rebuilding cost for insurance. More detailed surveys look for any signs of damp and wet/dry rot and likely sources, subsidence, may poke in cupboards and attic, move furniture and look under carpets. Could take anything from minutes to hours accordingly.
Writes the vaguest and most pointless waste of a document then charges you £500 for the privilege.
That's about it. My surveyor BIL refuses to do residential surveys as he says they're not worth the paper they're printed on. Ours certainly wasn't - 'may contain damp' actually meant 'riddled with the stuff, get out while you can, suckers!'
I'd get hold of a damp meter myself if I were you and stick it in some external and internal walls (about 1/2 metre up from the floor) - it's just a pinprick and is what surveyors are meant to do.
Sorry to be the bringer of doom, but at least you know what to expect. It's a legal requirement, so pay your £500 and hope your new property's habitable.
(if you know anyone personally who's a survey - ask around) you could always see whether they'll accompany you on a second visit as a 'friend' so that you can get a proper assessment)