superstokie13, welcome to FT.

If you’re travelling on BA certainly no-one will bat an eyelid, and nor will any other airline worldwide - there are many millions of places on the planet you could have been born in, and a check-in agent is certainly not going to know the spelling of each and every one of them.

So long as your call to the UK Passport Office has not resulted in your passport being cancelled due to you drawing the error to their attention, you’ll be good to go.

As this is more generally related to the UK & Ireland, and we have a dedicated forum for that, I’ll move your post over there where others will be able to add their own experiences.