Remove the rear triangle (try an impact driver on the allen screws, which I wish I'd done, or drill off the heads, which is bloody tedious, then screw an M10 tap into the bushes and drift them out from the opposite side), knock out the headset cups and take the three components to Argos. They do loads of them. Or come round and have a look at mine, which they did in candy apple red* back in 2011. There is no need to disturb the stem hinge or main hinge for a respray. Proper enamel doesn't jam them at all.
Caveat: the rear triangle can rust out under the powdercoat. On an old Brompton, inspect the inside of the tubes as well as you can (they're open ended). If it looks bad, buy a new triangle before the respray - they are not expensive compared with the painting cost.
*yes, red flam: red lacquer over silver paint. It's pimpy. Other tip; get them to aggressively face the head tube. If you can lose a mm top and bottom, you can fit a much wider range of headsets including - ahem - a matching red Chris King 2Nut.