It can be very worrying to discover that the tiles in your kitchen or bathroom contain asbestos. If this is the case, you have two options depending on the condition of the tiles.
If the Tiles Are in Good Condition
Don't worry about discolouration, but do look at the surface of the tiles and check all of them to make sure that they are not disintegrating. Tiles that are still intact are not going to release asbestos, and the best option here is probably to leave them where they are and cover up the entire area. You can do this using materials like vinyl, carpet or linoleum.
To be extra sure, some people also make up a sealant before they lay new flooring. PVA glue mixed with water to the point where it is reasonably easy to apply can be painted over the tiles and left to dry. This will seal the surface before you lay the new floor.
See a good online flooring company such as http://www.ukflooringdirect.co.uk for suitable new flooring types.
If the Tiles Are Disintegrating
If the tiles are in poor condition and are beginning to break up, you need to be very careful because they may be releasing asbestos into the air. You can get a professional asbestos removal firm to lift the tiles and dispose of them safely. This is a fairly expensive business, but at least you are sure that everything has been done safely with no risk to you or your family.
The Health and Safety Executive has more information on how to manage asbestos removal safely.
Alternatively, you can do this job yourself. Take the precaution of wearing a mask and goggles, along with old clothes that you can dispose of afterwards. Close the doors and windows. Don't hack at the tiles, as this will break them into smaller pieces and may cause the fibres to be released into the air. Instead use a flat tool such as a scraper to prise the tiles off in one piece. It may help to keep the tiles wet while you work on them, because this will prevent fibres flying into the air.
Double-bag the rubbish, with each bag sealed with tape. Your local council will tell you where the nearest waste dump for asbestos-contaminated items is.