Place of birth on British passport

I recently got my sons passport via online application since he was born in London and I am naturalised BC.

In his passport place of birth is listed the council he was born (REDBRIDGE for example).

I had also applied for my daughter 3 years ago who was also born in the same council but her passport says LONDON rather than council name.

Is it worth getting corrected my sons passport corrected to London or will council name cause any issues ? Both of their birth certificate says council name in birth certificate

Passport office link says they can mention town or city of birth per link below

https://assets.publishing.service.gov.u ... -birth.pdf

If anyone has gone through this befor me and advise would be of great help

Given that the British passport is valid either ways, why does the granularity of the entry (RedBridge vs. London) matter?

This information is going to remain on his passport for rest of his life and internationally people recognize London much more easily rather than local council name. Also it will give me peace of mind if both of my childrens passport is in sync (considering they both were born in the same council and same hospital)