The textured ceiling looks like artex although only a test will confirm if it actually contains asbestos.
The suspended ceiling I can't tell from images alone. Worst case scenario it's AIB panels depending on when they were done.
You cant tell if it's asbestos just by looking at it. You need to get a sample tested and a 10p size will confirm if asbestos is present. However, if you want to know the type of material, you need a water absorption test and at least a post it note size.
If you check check-a-trade you can get a rough cost per square metre. However, it won't be cheap so definitely use it as a negotiation point, especially as it's disruptive work as the room will have to be draped in polythene. Have a look at the Health and Safety website for more info on that.
Another area to watch out for are garages with asbestos ceilings and drainage stack cladding.
Don't let the agent or the seller fob you off. Ive done non licensed asbestos removal and there is quite a bit to it. To drop a garage ceiling for example, it's easily thousands to do it.
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