Anne are you near the Nrofolk Broads by any chance – I googled parsnip caterpillars and the swallowtail moth came up, which lives only in the Broads (apparently…).
What colour are the caterpillars? The last thing we need is something munching the leaves of umbellifers. It is only a few years since leek moth arrived and that has had a huge, bad impact in so many areas – many of mine are damaged already, earlier than usual.