British passport name change as per foreign passport

[ScoobyLondon]

My wife recently received her British passport but it had her name as per the foreign passport.

The foreign passport has now been changed to reflect the married name.

How do we apply for a new British passport to ensure the name change is as per her foreign passport? What documents should we include and do we need to include a covering letter, etc

Any advice on this, greatly appreciated.

thanks

[ScoobyLondon]

Could someone pls advise.

Thanks