When we moved to England with our two small children, we hired somebody to drive up from Devon to collect us at Gatwick. We told him we had a lot of luggage and he came in an estate (station wagon). Our bags and kids did fit in but only just barely. It wasn't that expensive and was well worth it. Normally we travel with our kids on public transport but moving is definitely a different story. The kids and I slept the whole drive to Devon leaning on each other's shoulders in the back seat, while my husband sat in front with the driver. I've never hired a car to go from Heathrow to Gloucester but that's a shorter distance than we did so it should be less expensive.