Surveyor Missed Something? Here’s What to Do

I’ve recently bought a house (first time buyer) 3 months in we’ve had a burst pipe in the loft, damage to the ceilings and a test via the insurance company was positive for asbestos, now I’m wondering should the surveyor have picked up in that the house if it’s age and the ceilings downstairs and upstairs should of been checked or advised for asbestos testing? If so and this hasn’t been brought to my attention when purchasing the house, is the surveying company liable now to fix this problem?