HSE's guidance on asbestos surveys is HSG264, Asbestos: The survey guide (HSE). It describes two types of survey.
Management survey
Finds and assesses asbestos that could be damaged or disturbed during normal use and routine maintenance. It is largely non-intrusive. It is the standard survey for a building in normal use, and the one buyers or owners of pre-2000 homes often choose for peace of mind.
Refurbishment and demolition survey
Needed before any refurbishment, renovation or demolition work. It is fully intrusive – the surveyor may lift floors and open up walls and ceilings in the area of work – so that contractors know what they'll find. HSE guidance says this type of survey is needed before such work begins.
Sample testing
If you're only worried about one item, such as an Artex ceiling or garage roof, a single sample tested by an accredited laboratory is usually cheaper than a full survey.
Do homeowners have to get a survey?
The legal "duty to manage" asbestos applies to non-domestic premises and the common parts of residential blocks (HSE), not to the inside of a private home. But if you are having building work done, the contractors you employ have duties to find out about asbestos before they start.