I will be walking alot, there is a footpath that runs all the way up to the top of Bexhill road. But it seems to start a little further up Falmer road, not right outside the Amex
Walk to the traffic lights and cross the Falmer Road, walk towards the village and there'll be a chicken shed and field on your right. Once past this, there'll be a hedge and then a gate on your right. Go through this gate - this takes you onto the path.
Once you've got almost to the top of the hill, the path will come to another gate. Go through this and join an 'unofficial' path that now runs along the grass verge of the Falmer Road.