1/6th the personnel does not equate to 1/6th the capability.
During the Cold War when everyone was expecting the Third Shock Army to roll across Germany, they had massive numerical superiority on paper. The difference was, the vast majority of our armour worked and was ready for action. Their armour was rusting, short on fuel, parts and ammo and crewed by soldiers who generally couldn’t care less.
As for British defence spending, yes we don’t get very good value for money for several major reasons:
1) We don’t order anywhere near enough kit to enjoy the sort of economies of scale that the Americans enjoy
2) Pork barrel politics ensure that we spend way over the odds for Brit produced kit, even when there is a proven foreign made alternative at a fraction of the cost
3) Governments with short-termist outlooks (so all of them) order delays in projects and/or last minute redesigns that greatly increase the eventual cost in order to balance the books
4) Too many at the top of the armed forces/MoD have one eye on a job with a defence contractor. In turn defence contractors stuffed to the gills with ex-top brass and MoD mandarins. Effectively, procurement becomes one big backscratching exercise
5) BAE. Not known as Big and Expensive for nothing