I don't have any experience of veg patches yet, but you can get plenty of young veg crops off market stalls at the moment, lettuce, cabbage, replacement spinach and broccoli, or you could probably do radishes or lettuce sown from seed. I think after brassicas you're supposed to sow legumes, so maybe buy some small pea plants?
I would go to your local garden centre and see what veg plants they have. Our local one had loads. Alternatively, read the back of all the seed packets and they will say when things can be grown from. I just sowed lettuce, beetroot, spring onions, spinach, cabbage, peas and cauliflower last week from seed (second sowing), and most are just starting to come up.
I've just ordered some purple sprouting broccoli, cabbage and leeks (small plants rather than seeds) to go in in July, with a view to overwintering them. I've also put in radishes and beetroot in the last week and salad leaves should all be fine at this time of year. If you;re in the south you might get away with french beans.