NY wrote

I have a Spear and Jackson lawnmower with a 125 cc Briggs and Stratton
engine (this one https://www.argos.co.uk/product/7597004). After a year's
perfect service, the engine has suddenly started coughing, spluttering and
backfiring, and sometimes repeatedly stalling as soon as it tries to cut a
trivial amount of grass (paradoxically, it cuts longer grass without
batting an eyelid).

Bet that last detail is crucial. Likely it has an automatic load control
that applys more power when the engine slows down and that
has failed so that it only works properly with a significant extra
load and isnt getting enough fuel on a light load.

At first I thought it was running low on fuel, because the uneven running
sounds identical to that which leads up to running out of fuel.

And that is crucial info too. Something is producing
that situation on a light load but not on a heavier load.
Almost certainly the speed control given that it cant
be fuel starvation on the heavier load.

But there was plenty of fuel. And the fuel is about 1 month old - it's not
been standing around for ages for its most volatile fractions to
evaporate.

And wouldn’t produce that effect at different loads.

I found several things that *could* have been the cause - but weren't.
There was a build-up of grass mowings stuck to the underside of the mower,
which could have been making the blade harder to turn -

But that shouldn’t see it work fine on the longer grass.

fixed that but the problem persisted.

Unsurprisingly.

The air filter could have been blocked

Again, that should see it not work properly
on the longer grass that needs more air.

- the sponge filter looked clean but was dripping in oil, so I cleaned it
in hot soapy water and gave it a *light* coating of oil as the manual
says, but to no avail.

Unsurprisingly.

The sparking plug was coated in a thin layer of black carbon, but the gap
looked OK and there was no coking-up of the contacts

Again, unlikely to see the problem only with normal grass.

I cleaned the carbon off the underside of the tag and the end of the rod
(ie the surfaces between which the spark jumps) but that didn't help
either.

Unsurprisingly.

I've got it to a state where the mower will usually run for tens of
minutes, with irregular misfiring and occasional backfires, but will
suddenly stall without warning,

Presumably because there is no fuel getting thru.

usually when cutting short sparse grass, rather than when it's working
harder to cut denser or longer grass.

See at the top.

And once it starts stalling, it does it repeatedly. My impression is that
it seems to be using a bit more fuel and that the smell of the exhaust is
stronger, so could the mixture be richer? The regulation of speed (ie the
governor) seems to be as good as ever:

But clearly isnt delivering enough fuel with normal grass.

when the mower encounters tougher grass, the engine note gets louder but
not slower.

I've tried with the drive to the wheels disengaged (ie I have to push the
mower) in case that was a factor - but it made no different.

Unsurprisingly.

Any ideas?

The problem is in the speed control. When it should be
delivering not as much fuel it is delivering very little or none.

Is it time to "get it looked at"?

If you arent confident of seeing what is wrong with the speed control.
They arent the easiest things to work on when they have failed.