Rhys
The simple answer is I don t know. There are too many variables; rainfall, temperature, pest cycles, soil type, etc. What can seem like the way to success one year, often results in failure subsequently. I see green manure as one part of the jigsaw, where a healthy, productive, living, growing medium is the objective. As a one off sowing, green manure is unlikely to make a big difference to a following veg crop but by continually rotating it over the seasons and regularly applying the resulting compost to the surface your soil will improve. Finally; try not to let winter rains deplete the topsoil, avoid bare ground, sow an appropriate green manure to stop minerals and nutrients leaching away. Re, phacelia; it covers quickly, provides organic bulk for composting and bees love the flowers. Field beans will add some nitrogen if left to mature and I have recently started using it as a vegetable crop in its own right, drying the beans for use in the kitchen.
Compostpope
A big area of broadcast lucerne sounds daunting! It will easily grow through a 4 in mulch. Rotavating will do a job but pulling out the regrowth along with weed seeds brought to the surface will take some time. Worryingly a lot of people would spray with glyphosphate or its frankenstein child resolva, (at our local garden awards evening, last week, the guest speaker from a nearby garden centre was extolling the virtues of that!). So covering with plastic is probably the only option. I think I would use the permeable woven fabric.
Pete