Things I've tried
clover- might be nourishing the soil but didn't suit me at all - doesn't keep the weeds down and has ambitions to become a weed itself.
phacelia- bees like it, pretty, a bit hit & miss depending on weather.
field bean- weeds grow up between it, so it makes a lot of work. Fibrous stems don't rot after digging in.
lucerne (alfalfa) - tried the first time this year. Fairly clean soil I sowed it in, germinated very well, not looking weedy atm, will report back.
Also bear in mind it doesn't have to say 'green manure' on the packet. You can fill a bare area with leftover seeds that you think will have got too old to sow next year. Anything non-invasive & in the right rotation group can be closely sown and dug in. A mixed pea forest loosens the soil up nicely!