Basic ideas off the top of my head:
Swede - boil and mash with butter and S&P, like mashed potatoes
Parsnips - roast, like roast potatoes
Leeks - really good in
risotto!
Beetroot - boil and slice to go in salad
Broad beans - boil and eat! you can also make
a lovely dip by mashing them (I add peas)
Scallions/Spring Onions - use in potato salad, in soups, stews, etc.
Celeriac root - mash either mixed in with potatoes, or on their own
Redcurrants & black currants -
summer pudding!
Gooseberries -
gooseberry fool!Tayberries - are they like blackberries? if so, make a crumble with apples
There are LOTS more ideas. As balmerhon said, the BBC food site is a good start!
(Edited to add links)