Stick to Irish or Scottish if you must, but English song has a stronger tradition of harmony singing. Gaelic song (which is the only type that could reasonably be called "celtic") is often ornamented in a way that doesn't lend itself to harmonies.

Many shanties (like Leave Her Johnny) are good for harmonies, but you'll find that most of the British ones are English - there isn't exactly a strong Celtic naval tradition.

Why get so hung up on "Celtic?" It's a very dubious category anyway (it's not a race, it's not a country, it's not a single identifiable musical tradition). Keep an open mind, look a bit wider and you'll find a great selection of suitable songs.

Marje