Hey,
My bike is still under the manufacturers warranty but it's time consuming taking the bike to the shop when I have limited time at weekends. So, any Brompton owners had this before?
My bike is a 6 speed. It sometimes has a problem moving to the second of the two sprocket gears, the smallest cog. Over winter with dirt all over the place and using a wet lube this seemed to start happening weekly. It seems as if a little dirt gets on the pulley holder, which holds the pulley that gets pushed side to side to change the gears, and when the gear is changed to move the pulley across to align with the smaller sprocket there's just not enough force in the spring(or mechanism) to force it across far enough for the gear to change. Sometimes if I ride it a while it suddenly starts working.

I now use a dry lube as I found the wet one I was using was going too waxy and it was worse with that lube. On Friday when I left work after unfolding the bike it took like 10 seconds to move to the second sprocket but after using it a bit it was fine again.

It's a bit annoying as weekly I'm ensuring the sprocket holder is clean, including spraying WD40 on it, which seems a bit extreme given I'm only using it 5 days a week, about 3.7miles a day.

Although dirt seems to be not helping I think there's just not enough force to force the pulley across far enough all the time to allow the gear to change.
The other day I thought it was in the second gear, started accelerating past another cyclist and "crunch", it then decides to move to the smaller sprocket(2nd gear).
I've tried adjusting the two small grub screws to adjust the stop, but in second gear it's not even touching the stop anyway.
Monday, with a nice clean bike, freshly lubed chain and clean pulley holder I know it'll be fine but by Friday it may start happening again
Anyone had this before, and got an easy fix without dumping it back with the shop?

Dirt gets onto the plastic chain pusher that is bolted on to the chain stays. There are two ledges on it that act like a shelf. The dirt acts to stop the set screws which adjust for setting the gears. Instead of hitting the plastic sides of the shelf they are stopped.

Also, after a short time, the cable stretches. There are notches inside the shifter that adjust the tension. There is a video clip of how to do this under Support on the Brompton site. However my first suspect from your description is the cause is dirt.

Sometimes the shifter cable binds inside the cable housing. I find a little synthetic motor oil on the cable helps prevent that.

I have also had an issue where the bushing that the jockey wheel (the one that is pushed be the chain pusher) gets worn and ends up looking bent. Replacing the bushing made the shifting much more reliable.