The FDA define cheese in 21 CFR 133.
CFR - Code of Federal Regulations Title 21 (fda.gov)
It has always amazed me how uncheese like cheese is allowed to be, for example requiring only 23% of content to be milk based, other components can be generated from cheaper sources.
Perhaps one day you will discover which part of 'cheese' you have a problem with. If it is only cooked cheese, then it would appear to be one of the compounds generated by the cooking process. This is unfortunate because cooking is *complicated* and generates a lot of different compounds (in the same way that tobacco smoke is a lot more complicated than tobacco).

You do have the option with BA to select a Low Lactose meal that avoids cheese and milk
Special meals | Food and drink | British Airways