Hello and welcome to allotmenteering!!
Totally agree about planting garlic in Autumn- you'll get a much better crop!!
Beetroot- you might have to thin! A beetroot seed is actually two seeds stuck together, you'll notice that every 'seed' produces 2 seedlings. Don't allow the dirt to get too compacted and it should be easy. I like to leave space next to my row of beets to create a second row from replanted thinnings.
Cabbages- i like to start mine in trays, where i can control slugs more easily, then plant out when they have about 4 leaves. can pick the strongest seedlings then too.
Leeks, start in trays and put into final place around June. I use the dibber to make holes about 4-6 inches apart and just drop the leeks in- they sort themselves out from there!
Alternate your rows of onions with your carrots! The onions deter carrot fly, and the carrots deter onion fly. And the onions help you see where your carrot rows are coz they take an age to germinate. Covering with agricultural fleece is good too. I put my carrot rows about 6 inches apart, and pop a row of onions between them- they don't really compete much with each other for space.
POtatoes- highly subjective to taste. I really liked my Maris Peer this year- i could furtle around and get a few small new potatoes out and leave the rest to get bigger. they mash well, and were pretty resistant to scab and pests.
I also left my Lord Rosebery second earlies to get bigger and some got huge! Nice and fluffy too when cooked. Not too waxy. I prefer floury over waxy for mash.
Tomatoes- sow in feb/mar indoors- i plant out in late May when all chance of frost is gone. Keep them far away from your potatoes as possible- to reduce blight infection
I notice you don't have french beans on the list. If you do decide to grow any, i heartily recommend Cupidon, available from realseeds. They produced a hefty crop for me, and don't go stringy when you let them grow big!
Good luck