Ask them just what the levels are - get them to check the ambient (background) CO level when the boiler is off.
Ask them to show you the calibration document for their test equipment.
Ask them if there's a legal upper limit or just a British Gas invented limit and if there is a legal requirement ask them the regulation that applies so you might check.
Get a CO monitor of your own - contact the local council.
After reading BG stories on here I would be more concerned about BG trying to sell me a new boiler + Installation (£4000) than I would for my health.
BG may be right and it's not a good idea to take unnecessary risks with CO the silent killer - but the flame is blue and BG have been doing the servicing - it's the "fluctuating up and down" that sounds rum - that smacks of a defective detector rather than a wobbly boiler. Ask if they can check it out with two detectors so you can compare one with another.
I know nothing by the way but have a healthy disrespect for BG.
Peccavi
June 2009