What UN agencies are in the UK? There are also some other multi-national organizations worth looking into.

If you're working for a UN agency or another multi-national organization, you don't need a visa at all. It has always been an old fallback here in France - if you can find a job with either the OECD or UNESCO (both in Paris), it doesn't matter if you have a visa at all. You automatically have the right to live in the country as long as your job at the agency lasts.

It can become a problem for some who work like that when they retire. People want to stay in the country they've lived in for 20 or 30 years, but they have no rights to once they leave their job.
Cheers,
Bev