<<< Onions, carrots, parsnips, celery, lettuce, beetroot, turnip, swede, spring onion and radishes are sprouting now and I have a load of potatoes ready to go in as soon as the weather turns
2nd March and still snowing here! >>>
Yes it's pelting with snow here too, but not too cold.
The onions, celery, lettuce, beetroot and spring onions will be fine started off that way. In fact I start off several batches of beetroot in modules, with about 3 seeds per small module. Once they have a few true leaves I plant them outside, with protection mainly from nibbling. They grow in small clumps, but still develop big roots, just space them further apart.
Starting radishes in small pots or trays won't work well, but if they're only just coming through you can prick them out into deeper pots, about 1-2" apart in the pots. They are frost tender though. The same technique might work for the carrots and parsnips if they only have their seed leaves, but as pgkevet says, they prefer to be sown where they are to grow.
Prick out the swedes and turnips now, the swedes into at least 3" pots and get them outside as soon as you can, but they are usually sown in May, otherwise they may go to seed.
I so understand your excitement to get stuff in the ground. Don't worry - we hardened gardeners get carried away too. Don't worry if all or some of this lot fail - seed isn't expensive, just keep that enthusiasm going
Celery is best started off in modules, so you're fine there, potting up into 3" pots then planting them out after the frosts.
Onions are fine started off in modules if they're sets, or in deep modules (leeks too) if seeds and the roots can get quite crowded without setting them back.