Sow in a heated propagator, in a warm place, or directly in tunnel soil when warm enough:
For polytunnel or greenhouse cropping, or for planting outside under cloches or fleece at the end of May
French beans, runner beans, sweet corn, courgettes, edamame (soy) beans, cucamelons, gherkins, pumpkins, summer squashes, marrows and melons. You can still sow cucumbers and tomatoes for late tunnel/greenhouse crops. Also herbs such as basil, coriander, dill, Greek oregano (best for flavour), lovage, mints, parsley (giant flat leaf Italian best flavour) Perilla (Japanese beefsteak plant) and fennel, Alpine strawberries (Reugen best variety) Florence fennel and half-hardy single flowers such as tagetes, French marigolds, nasturtiums etc. for bees and butterflies and to attract other beneficial insects like hoverflies etc. to help with pest control and pollination, both under cover and out in the garden.
It's really important to shade propagators and young seedlings from strong sun at all times now to stop seedlings from cooking! - You can also switch off propagators during the day to save energy - even if shaded on sunny days they will be plenty warm enough - but do make sure you remember to turn them on again well before it gets chilly in the evening.
Sow in modules, in a seedbed for transplanting, or in the ground where they are to crop, if the weather and your ground conditions are suitable:
Asparagus, globe artichokes, beetroot, broad beans, carrots, all varieties of peas, savoy and other autumn/winter cabbages, all varieties of sprouting broccoli including calabrese and purple sprouting, cauliflowers, salad onions, Hamburg parsley, landcress, lettuces, perilla, orache, chicory, kohl rabi, kales (those for cropping overwinter outside from the middle of May onwards), parsnips (early May) radishes, rocket, salsify, Swiss chards, spinach, turnips and swedes, summer purslane, lamb's lettuce, salad mixes and perennial hardy herbs including sorrel. Asparagus peas, cardoons, Good King Henry and New Zealand spinach can be sown outside under cloches now, and also from the middle of May, if the soil is warm enough, sweet corn, French and runner beans. Marrows, courgettes, pumpkins, ridge cucumbers and squashes can all be sown outside under cloches at the end of May, in warm areas. Also sow some single annual flowers such as limnanthes (poached egg flower), cosmos, calendula, Californian poppies, convulvulus tricolour, nasturtiums, phacelia, sunflowers etc. to attract beneficial insects like hoverflies and ladybirds which will help with pest control, and also to attract bees which help with crop pollination. Sow fast growing green manures like buckwheat, mustard (a brassica so watch rotations), lupins & red clover (legumes) and phacelia, to improve the soil by adding humus, to encourage beneficial microbes, 'lock-up' carbon and feed worms (after digging in), on any empty patches of ground that won't be used for 6 weeks or more.