Yes, we did, but about 13/14 years ago, so things may have changed. I went, as suggested to our local council. I think I rang up and explained and they put me through to the relevant person.
I can't remember their title, but they explained how to get a licenced contractor. There was one locally - but I think they tend to be part of bigger companies because the investment things necessary for asbestos removal is significant, but it may sit idly for awhile.
I am also sorry that I can't remember the name of the company - the paperwork stayed with the house - but that may well have changed.
So my advice is to begin with your local council - I am sure they will still be offering this advice via phone or the internet.
I should add that as soon as preliminary work began, we had people knocking at the door offering to take it away cheaply. I also had one acquaintance tell me that I was 'daft' to pay so much when his mate would have done it. I told all of them, truthfully, that one of my dearest friends had died of mesothelioma, which I would wish on no-one.
You haven't said what kind of asbestos it is - I am aware of different procedures, but as it is sometimes uncertain, just contact the council for guidance.
I'm sorry this is not as helpful as it might be, but no-one has come forward with a more recent experience.