Disclaimer 2002 so easily could be out of date.
There is (or used to be) a QR which the staish or his/her nominated deputy could sign off to have anyone have a second job at any time, assuming it did not interfere with their RAF duties. Prob meant for lower paid workers, but I used it (signed off by OC Admin Wg) to have dual employment for the last 7 months of my RAF career (I was a Sqn Ldr) by then.
There was much wailing and gnashing of teeth from the Resettlement Officer who was not impressed with me sailing over his head, but it happened so it is (or was) do-able.
It probably helped that...
I had accumulated all the leave I could (stopped work on Sqn about 4 Nov, [started my new job same day] and was immediately replaced, left RAF mid May the following year 2003).
I had good relations with all the key players (Sqn Boss, Staish...most of all the Chief Clerk). Not the Resettlement dude tho lol
I was swapping to a MOD Civil Service position to the benefit of the RAF
Maybe this avenue is closed off now...I don't know.
As for tax...been doing my own return since the day I left...don't know why this is even a thing???
And yes, several years later...and totally out the blue...
However, HMRC (our whoever they were then) kindly wrote back saying "We notice you paid NI twice during the period blah (of two jobs), so we owe you some money!"
...I got this too! Four hundred beer chits as I recall 