I'm sorry, but that's tripe. Since 2010, the number of civil service jobs in London has increased. There is no reason whatsoever why even the most specialised employers could not re-locate to any of the major urban areas in Britain, and expect prospective employees to follow them. Or else how do you explain why other European countries generally feature a range of cities, much smaller than London, but many as economically successful ? The 'need' to concentrate all economic growth in London is a self-sustaining myth which is doinf this country untold damage
I was mainly talking about the private sector but:
The bonfire of the Quangos in 2010-12 lead to a large number of quango staff becoming civil servants (again) when some Quangos were reincorporated into Departments, there were at least 6-7 adsorbed into DfT for example, so that need to be taken account of when you use those numbers. At that time there was also some restaffing of National Statistics to London after the failed Newport move when lots of the staff didn't move and they couldn't recruit locally.
The current global trend suggest otherwise with large city agglomeration correlating with higher growth rates (taking account of population change effects). This isn't a London vs the rest of UK issue, it is UK vs the rest of the world issue. Take my wife firm for example they move jobs out of London by deskilling the work and getting it done in Mumbai and Warsaw (the later now becoming more popular as they can't get enough good staff in Mumbai)
In many more specialised sectors it is quite common to have employees whose partners also have jobs in a (different) specialised sector hence the chances of both partners moving is slim (see Nat Stats problems). People also want employment options with more than 1 firm hence Leeds and Manchester doing well in accountancy and law jobs due to the multitude of firms. Many employees also don't trust firms to change their mind again in few years and don't want to be left stranded.