Just because nobody mentioned:
Get a proper grease gun, I know it's a british car, but for the grease gun I rely on german workmanship.
I have one of
those by Mato.
Together with an appropriate 500mm hose like
this, greasing is easy.
The hose snaps onto the grease nipple and no further pressure needs to be applied during greasing.
My narrow 4/4 tires help, may be trickier with the wider ones of the +4 and Roadster.