Thanks for the great advice. I've learned a lot about whitewall construction today.
Tried the solvents but the texture was the problem and getting the gunk out of the pores was going to be an ongoing problem.
Apparently whitewalls are cast under the outer layer of black rubber and the surface is skimmed off to reveal the white. On the Maxis tyres I have the skim left a texture like chatter you get with a blunt lathe tool. I tried the wet and dry with soapy water but ridges at either side of the white left marks on the inside and outside of the white area. I ended up grinding the ridge using an air finger sander then blocked the white smooth. This appears to have left the finish smooth and in the future I hope I'll be able to just clean with a solvent.
While I had the wheels off I took the opportunity to clean the spoked rims. What a pain!
Thanks again to all that provided advice.