Thanks Elynor. It turned out that my niece likes ethnic food, after all, and we ended up at the Sheesh Mahal, my hubbie's favourite restaurant. They do some vegan food there. But we'll possibly check out the Lime Tree next time around.
We also found a place in York called El Piano, I think, that did lots of vegan stuff. It was good, and even managed to satisfy my DH, a committed carnivore.