The portable generator is designed primerally to provide a 110V center-tapped earth supply as is normally used on UK construction sites. The 230V output is something of an afterthought which is why you end up with it referenced to earth in a weird way.
In the standards for modern appliances in Europe there is no expectation that the "neutral" pin is at earth potential. So powering modern appliances off the generator should be safe.
OTOH in UK house wiring it is normal to assume that neutral is at earth potential. We don't normally put any overcurrent protection in the neutral and we frequently work on circuits with only the live isolated.
As I see it you have a couple offew options, neither of them greateach with it's pros and cons.
- Make sure all circuits are RCD protected with a double pole RCD (note that most RCBOs are only single pole isolating) to mitigate the lack of overcurrent protection in the "neutral" and place warning notices so people don't try to work on circuits that are only single pole isolated.
- Set up the consumer unit with double-pole breakers. This is a good option electrically but can get kind of costly as double pole breakers are not widely used.
- Modify the generator, remove the existing earth reference and add a new one at the neutral end of the winding. Downside here is you will almost certainly be voiding the warranty and the 110V output will no longer be the center-tapped earth supply expected on UK construction sites.