oooh, well, since you ask 
So far we have only removed the bath panel, because we need a new bath. If we hadn't needed a new bath we would have left it, as someone said, I don't think it is dangerous if it is encapsulated (it was within the concrete of the bath panel) and undisturbed.
I thought that the council might help us as it might be classed as a sort of public health issue. The council said they would dump it for us, if we left it at the boundary of our property double wrapped and sealed. But we had to get it out ourselves - or get someone to do it. The council did give us a couple of companies to ring to do it. The first one quoted £480
; the second one £80. So we used that one! He took it away as well.
The other stuff we will deal with when we get round to decorating the other areas of the house.
Yorky, I would start with an Asbestos survey. The council might give you some contacts of reputable companies that do domestic work. In our case, we used the company that the council themselves use for their social housing. I thought if the council use them they would be reasonably priced and safe. I did get quotes from two others though to compare costs. Our one cost £210 and they looked at the whole interior, and took samples where they were suspicious. Took about an hour, involved two people, and then they emailed a very long PDF document of their report.
Regarding removal if Asbestos is confirmed, maybe call the council again to see what their advice is, maybe it falls under Waste Management (it was this in our case), or maybe Building Regulations: they might be able to recommend if you need a specially equipped builder, and maybe give you some contacts.
Hope this is all useful!