I'm a fully qualified asbestos surveyor (p402, s301) and consultant and have been since 2003. What Spud up there says is good advice.
I see horror stories all the time of poor, overcharged and unnecessary removal, even today with the new legislation. People with a 'bit' of knowledge can be a dangerous thing.
BUT I also occasionally see people living with asbestos in horrendous condition exposing both themselves and their families to fibres on a daily basis
If you are planning on any kind of refurb in the property, get an intrusive (now known as a Refurbishment Survey rather than a 'type 3') survey done by a UKAS accredited company. This way you will get to know exactly what you are dealing with and whether you need any remedial work at all. A good surveyor will advise you on the best course of action - but take care, many removal companies have their own surveyors who will tell you the worst. If you require a survey before purchase, it is unlikely a Refurb Survey will be suitable as these can be very destructive and tend to involve damage of decor etc. A 'Management' level survey (formerly known as a Type 2) will at least give further information on the boarding. It is not unlikely asbestos insulation board (AIB) is associated with the flue and used as fire breaks in a property of that age. Good information on AIB can be found here:
http://www.hse.gov.uk/asbestos/essentials/aib.htm
You don't necessarily need to have the asbestos removed unless it is in bad condition. Small damage may be repaired by yourself and the legislation doesn't cover domestic settings in the same way as in a commercial setting at the present time (this may be subject to change in the future and may be considered if this is an 'investment property').
If you want any information, I'm happy to help. Obviously I can provide a quote for a survey, if required - depending on the size of the property (4 bed can mean a lot!) and the location - I'd say £275-£400 for a UKAS accredited survey is a about right.