Just to bring together some of the above information (and, hopefully, to add a bit too):
National Express service 040 generally runs only as far as Bristol. However the 1730 (daily) service continues to Burnham-on-Sea, calling at Highbridge (Church Street, opposite the cemetery) at 2130. (Due to route variations, the arrival time is actually 2135 on Monday, 2145 on Friday and 2120 at weekends):
https://timetables.nationalexpress.com/routes/SH/040/London-Burnham_on_Sea/O/pdf
The return service runs at 0908 daily:
https://timetables.nationalexpress.com/routes/SH/040/Burnham_on_Sea-London/I/pdf
At other times you'd need to travel to Weston-super-Mare (see links above for timetables) or to Bridgwater. There are 3 services per day to Bridgwater on route 502:
https://timetables.nationalexpress.com/routes/NX/502/London-Westward_Ho/O/pdf
Return services:
https://timetables.nationalexpress.com/routes/NX/502/Westward_Ho-London/I/pdf
Weston-super-Mare is 11 miles from Highbridge. Bridgwater is 8 miles from Highbridge.