PCP SHooter;
"I also do not think relocating Grey Squirrels or Rats is legal as absolute pests"

Grey squirrels certainly have to culled, not released alive, experience of my late Aunty with local Authority pest controller and recent "phyco Squirrel' incident in North wales (?) Her daughter in law did relocate mice caught in 'captive traps' about 200 yards, then wondered why she had just as many as started with, explained they had homing instincts like pigeons 😉
Poisoning works till they become wary, but decaying carcasses cause a stink . Shoot & remove, if can change invironment that attracted them in first place