Filton is a building site now, Almondsbury is very much Police/HEMS only, nearest I can think of is the museum at Weston-super-Mare…..that is not close to Severn Beach. The 1/4 mil shows two at Avonmouth and Berwick Lodge. Have you tried Helipaddy? I don’t have a subscription but may be worth a go.
https://www.berwicklodge.co.uk/