The place name in Kent you are looking for is probably Anderide, near Pevensey, found in the Anglo Saxon Chronicle. It is not a modern place, though it was apparently a largish settlement at the time. At that time, it would have been surrounded by woodland as most of England was originally covered by primeval forest. I think it is mentioned in Rudyard Kipling's "Puck of Pook's Hill", where I imagine your children may have got the name.

There appears not to be much primeval woodland left in England (see hereArchaeology), though there are some patches of old woodland in other parts of England ... Wychwood, Woodland Trust, Trails.

Cheers!
Ian