As jonathan says, chuck size refers to the diamter of the main body. Depending on jaws, you can hold stuff bigger than the chuck diameter, but it's not always advisable. 85mm parts should be quite comfortably held in a 4" chuck.
Lathe capability is more important that chuck size. Lots of smaller lathes rely on electronic speed control, so are pretty useless for dealing with larger diameter parts as at low speed they lack the required torque to handle decent cuts. I'd personally look for something where speeds can be changed via belts (gear change is probably out of your price range) to make the lathe more versatile.

If you're wanting the lathe urgently, I'd be checking Arc Euro Trade, Axminster, Warco, and Chester to see what models they do that would suit your requirements, then making some phonecalls to see how quickly they could deliver.