If there are three or more people coming as a group and one of the group is happy to drive in the UK, then you could possibly save some money by hiring a car, although, obviously, that does then mean that you have to find your way to Minehead on your own. You can currently hire a medium size saloon car for about £60 upwards, and then petrol will probably be about £45 on top of that. Details of the car hire companies operating from Heathrow are
here.