The're looking good Mikey and they should all do well in raised beds.
Carrots won't like being moved, I'm afraid; the long taproot is formed very early and will be damaged if you move the plant. Best to sow them where you want them to grow. But give it a try by all means. I should sow some more though, in rows outside.
Leeks and cabbages, on the oher hand, positively benefit from being moved in my experience.
The leeks can stay in their trays till they're a few inches high. Then harden them off and move them outside, possibly into a nursery bed, or where you want them to stay. Make a hole a few inches deep with a dibber; trim off excessively long roots with scissors and drop a leek in each hole. When you've done them all, gently fill each hole with water. Don't fill in with soil. This gives them room to expand and makes those tasty white leaf bases. (If you're going via a nursery bed , you only do this rigmarole when you finally put them in their permanent homes!)
Cabbages like firm soil and lime. Very carefully transfer each one to a large module or 3" pot when they have a couple of proper leaves. After a few more weeks (when thhave about 5 leaves) harden them off, then sprinkle a little ground limestone in the planting hole and plant them firmly and deeply - right up to the first leaf or even a bit more. Firm them in well and give them a good drink. Then have one yourself. Dont forget to net them or the pigeons and caterpillars will have the lot!