I just searched gov.uk and found this.

4. Definition of a damaged passport

A damaged passport is one which isn’t in a condition to be accepted as proof of identity.

Damage may include the following:
details are indecipherable

the laminate has lifted enough to allow the possibility of photo substitution

discolouration to the bio-data page

chemical or ink spillage on any page

missing or detached pages

the chip or antenna shows through the end paper on the back cover for the new style e-passports

the chip has been identified as damaged after investigation

https://www.gov.uk/government/public...ssports-policy

Not sure how far from LHR you are but it might be worth going there tomorrow and asking BA if its acceptable in its current condition?