I left Bournemouth in the late '70s and cant remember any pedestrianised areas in those days
It was the R A B at the top of the hill at the Old Christchurch Rd (police station end of town) - there used to be a night club and Burger joint called the Alcatraz on the right hand side of the road just before the R A B - the gun shop was probably about 400 yrds back down the hill were the road bent.
Many happy days spent in Bournemouth in my 20's
Cheers
( ;-)>