A few options to consider:

If your current grips are loose you could wrap a layer of friction tape on your bars and reinstall the grips.

You could buy another set of grips and cut them to length

You could also use bar tape but it's intended for wider diameter bars and may not be as comfortable on your Brompton. I know Specialized (and probably others) made these gel inserts that would fit between the bar and the tape to give it more thickness. That might be an option for you.

Handlebar tape when properly done will stay in place just fine. Personally though, I'd just cut off some regular grips.