Which manufacturer was it? I've had that problem with cheap plastic toy cars, but not with figures. However, it does sound like the plastic is still leaching chemicals

You could try cleaning them with isopropyl alcohol to see if that has more luck. It may even be worth running them though a paint stripper like detol.
My only primer suggestion would be something like Valspar, which is designed for soft plastic like patio furniture. However, it's an acid etching primer and leaves the surface quite rough. That's not an issue for a conversion of a Poundland vehicle, but I'm not sure what it would do to the detail on a figure.
Just another thought, you could try sealing it with pva before painting/priming, although again, that could cause problems with details