Is there anything I can do about this?

[HollyDollyDolally]

Paid for a category 3 survey and it's come back that the house is inhabitable, mainly due to significant subsidence and rising damp. Vendor wouldn't reduce the property so we've pulled out. The house is back on right move today at full price.

Can the estate agents do that?

It feels incredibly wrong that someone else will be in our position, months wasted and out of pocket or worse, buy the property without a survey and be ripped off.

For future properties, if I ask the agent if any previous surveys have taken place, do they have to tell me?

Yep - a house I wanted to buy but came back with a lot of major faults that made it unmortgageable went back on the market four times at the same price with the sale collapsing each time before they gave up and rented it out. It shouldn’t be allowed!

A similar thing happened to us 2 years ago. A property had been on the market a year earlier (2022). Then it disappeared. Then it came back on. I asked the EA about this and they barefaced lied and said the owner had taken it off and refurbed it when they clearly hadn't. We put an offer on anyway as properties in our area were few and far between, and two months later the mortgage survey said it was unmortgageable because of significant damage to the exterior, including concrete rot which needed fixing urgently as portions of the rebar were exposed on a side of the property we hadn't been able to get to when we viewed.
The mortgage advisor at the EA was adamant we just needed to try a different mortgage company but I wasn't happy buying something dodgy, so I went back and viewed again, and saw that what the mortgage surveyor said was true. Pulled out. Assumed they'd sort out the problem or reduce the price and make it clear that it was for cash buyers only, but they didn't, they put it straight back on, it went under offer within 3 months, disappeared, then 3 months later reappeared, then went under offer again 4 months later, then 2 months later was back on the market again.
It then went under offer again and I stopped looking for a year as we bought elsewhere, but I just went to check and lo and behold, it's on the market again. Literally nothing has been done to it in that time.
No one can buy it and the EAs are misleading people and wasting their time and money, what on Earth is the point of wasting people's time and money like this?
There's nothing in it for the owners or EAs, they need to find a cash buyer or fix the building.