I think you would be pushing it for beetroot, but it might be worth a go if you can cover them. I’ve got a big insect mesh tunnel just emptied of onions and was considering turnips next. It is getting a bit late for them as well, but I have some cheap seeds I can use. If it stays mild, they grow fast and I am usually still picking them come the end of the year.
On my plot beetroot really do get munched going into autumn and I end up with almost nothing left to eat, whereas turnips usually get left alone.