Any children with British passports are Brits as much as you are, and will be treated exactly the same as you for entry to UK.
Only difference at Phils end is that they may have to pay the travel tax upon departure. Make sure you have their Phils docs with you at the airport as well as their British passports. (Immigration may want to have a look).
Last time I brought my step-kids back from the Phils in 2003 (Filipino passports), no medical checks needed.
