Will they be treated as home students for university as father is living in london and paying NIE , Council tax. Plus they are British nationals.
I'm a British expat and this question comes up frequently on the expat boards. As I understand it from those conversations a student has to have been resident in the UK for 3 years prior to starting university to qualify for domestic fees, less than 3 years and they pay international fees. The rule applies whether they are a British citizen or not and regardless of whether one of the parents has been resident in the UK because it is the student that must have been resident.
I'm pretty sure the rule does not apply if the student has been living abroad due to parent in the Armed Forces, diplomat etc. I think there is also some exceptions if they can prove the family is abroad on a "temporary" employment assignment by British based employer but I don't know the exact details of that.
From the Brit expat forums I have seen those who have had to pay International fees, those who have gone to university in other countries because they would have to pay International fees, those who have sent their child to 6th form in the UK and added a gap year in order to make the 3 year residence requirement and some who have had luck not being charged International fees despite not being resident in the UK for the required 3 years - but the consensus seems to be that is "luck" due to the university not understanding the rule, not knowing that the student has been non resident for 3 years, wanting the student so agreeing to charge lower fee, etc. so you could call it "luck" or breaking the rule or negotiating the price!
Hope that helps a bit and if your friend does an Internet search I'm sure there is lots of info out there and it comes up often on the BritishExpats forum.