Hi,
Your grid ref is very close to the highest point on the downs. I have plotted some lines from the Druid Stoke and from Ashely Down and the generated an elevation that can be seen here.
http://www.severnbeach.com/upthedowns.jpg
On passing the site i will drop by and have a look around for you.
There is also a road in Shirehampton called "Barrow Hill", sadly this site has been destroyed for housing.
When you draw a line from:
King Weston Barrows
Barrow Hill Road
Badocks
Ashley Down
There is a line of sight, very shallow to the point you talk about on the Downs (300ft). From the maps it looks like the highest point in Bristol. They must of have good field glasses ;-)
Regs,
Ike