Curiously, British work on VG seems to have arisen independently three times over, between 1945 and 1947.
First off the block was Barnes Wallis in 1945, beginning work on his "wing-controlled aerodyne", which he regarded to be a distinct type of aircraft from the conventional aeroplane. It drew heavily on his work on airships such as the R101 and their aerodynamic control and stability. He progressed from Wild Goose, with a very blimp-like fuselage, to the Green Lizard missile and eventually to Swallow. Not sure where the Science Museum's PRU version fits in, but it looks very much like a manned derivative of Green Lizard.
Two years later LE Baynes, designer for Alan Muntz & Co and best known for his Bat tailless carrier wing (which the world's most experienced tailless pilot Robert Kronfeld found a delight to fly), produced a complex VG concept design in which almost everything seems to have swung or swivelled in one way or another. Like Wallis' work, nothing seems to have come of it.
At much the same moment as Baynes began on VG, GAL engaged GTR Hill as consultant. The background to this is intriguing. Hill is familiar for his tailless swept-wing Pterodactyls, inspired by the pioneer safety aeroplanes of JW Dunne. The Pterodactyl IV had a short range of variable wing sweep for longitudinal trim. While Hill and Handley Page's Gustav Lachmann were sent to Canada early in WWII (where Hill designed the NRC glider and Lachmann was incarcerated as an untrustworthy alien), the UK had no remaining expertise in tailless aircraft. Nevertheless, the Tailless Aircraft Advisory Committee (many of whose members were old acquaintances of Dunne and Hill, and should frankly have known better) saw fit to commission some experimental types off GAL. The world's most prolific test pilot, Eric "Winkle" Brown, decreed the one he took up to be the most dangerous machine he had ever flown. It went on to prove his point by killing Kronfeld. In the light of all this, taking on Hill as consultant a few years later might just have seemed like a good way to avoid making the same design blunders again (my cheeky speculation as to motive, there). The result was a VG "transformable delta", whose successor projects appeared under the Blackburn name after that company acquired GAL. This was the line of development which led, via various routes, to all the other projects in this thread.