"though seems to use a hell of a lot of fuel for a 2 stroke " \
The Briggs is a 4 stroke and if it is running ok then leave it alone, changing the air filter is probably the only thing that will help with the fuel consumption
+ a
big one to this.
Odds on that the air cleaner foam has never been washed out, since new. So it may need replacement.
This makes the engine run very rich, and greatly accelerates bore wear as well. Used to see this on many small Briggs engines that used this air filter setup, back in the 1970's.
Most of the Briggs engined push mowers back then used a snorkel and remote paper element filter, and so avoided this particular problem.