You are right that a month ago you'd have had more time to clear the ground before the weeds really got going, but it's not too late.
I second the idea for an overall plan. Then maybe aim to get half (or less) under control & in production this year and the rest next. Cover the ground you won't clear this year with a tarpaulin and the weeds under it will slowly die and make clearing it this winter much easier.
For the rest, it's a real chore clearing by hand - Is it possible to get someone to skim off the top inch or two of soil (weeds and all)? Or how do you feel about weedkiller like Roundup? Either method will save quite a bit of work, but you then need to dig your beds and plant stuff out, clearing as much of the roots of the pernicious weeds as possible.
You are probably a bit late to buy seed potatoes, but if you do see some around you could plant first or second earlies as late as June/July not maincrop ones though - they need to go in now(ish). Potatoes are a good cleaning crop for the soil - digging them in & out & earthing them up etc all helps clear the weeds out of the soil, so it would be good to grow some if you can.
Now is a good time to plant runner beans/french beans inside in pots. Or you could plant direct outside from 14th May (a bit later if up north), but the soil needs lots of muck dug in.
You could get away with planting onion sets now I reckon, but don't leave it much longer. You can plant carrots, beetroot, kohl rabi, lettuce, radish all sorts in fact etc now and on succsessionally through the summer. Parsnips are traditionally the first crop to go in, but can still give good results if sown in April or even May. Cabbage, Sprouts, Brocolli etc. can go into seed beds now & then put into final position in June (or just buy small plants ready to go in June) - you would need to lime the soil pretty much now for brassicas.
Sweetcorn can be sown inside in pots later this month - don't put outside before June though as it's very sensitive to the cold and the same goes for courgettes and squashes.
So lots that could be planted, maybe choose a few crops that you really enjoy (or that save a lot of money) & focus on them this year?