I would expect the positions to move but filled with new hires from the Derby area personally. Not least because moving staff out of London makes it very hard to stop paying them London rated. You cam advertise a new post in Derby for a lot less than a Civil Service salary.
When the BRB was created in the 1960s it chose Derby for some of its new HQ functions; BR Workshops was first, and this was located in a now demolished office block located somewhere near were Zara now is in the city's main shopping centre! Derwent House and Trent House in the Railway Technical Centre were built specifically as HQ offices, and BR Workshops moved into Derwent from the city centre; however, the Supplies Department - which had only been established a few years earlier - moved from London to Derby (it was located in Eversholt House, the old Railway Clearing House building in Eversholt Street) and many staff moved north with it.
Regarding the last comment about salaries, it was reported on the BBC East Midlands regional news some time ago (I think just before Covid) that the Derby South parliamentary constituency had the highest average salaries in the East Midlands, and Derby is also well up on a national comparison; Derby South is the home of Rolls Royce civil aerospace, Alstom, and many specialist supporting contractors, all of whom pay well. Cross the River Derwent on the ring road from Derby South to Mid-Derbyshire, and immediately after crossing is Rolls Royce Marine, the nuclear facility which will be involved with propulsion systems the AUKUS submarines, and a short distance on is Balfour Beatty; and drive west along the A50 from Junction 3 to 4 and you've got Toyota's Burnaston facility (in the South Derbyshire constituency)
Largely because of its good road connections, Derby is a magnet for people to work in from a MASSIVE area; I've been retired for quite a few years, but in the last office in which that I worked there were people who drove into Derby from Coventry, Rugby (both via the M1), Sutton Coldfield (A38), West Yorkshire (also M1), and a guy who drove from somewhere west of Birmingham via the M42/A42. Of course there were also people who lived closer - Nottingham is less than 20 miles away - but I subsequently talked to a friend who worked at Rolls Royce and after pausing to think, he confirmed that his experience of people driving into Derby to work was similar to mine
So although jobs can be advertised in Derby for less than a Civil Service salary, it's unlikely they will be filled with people of talent when much higher ones are already paid in the area.