The Cavendish Deer-park?

I've been recently poring over the map of Suffolk produced by Christopher Saxton in 1575

This map was far ahead of its time, and was copied by all subsequent cartographers for over two centuries. One curious feature that he recorded was a Park at Cavendish. When John Speed copied the map for his 1610 'Suffolke Described' he left out this park, so it has always been assumed that it was an error. However, I've always been slightly bothered by it. Barring the transposition of two parishes, Saxton didn't make many errors: The park seems to be placed quite near where Houghton Hall still stands today, and it is clear that the building that stands there now is but a small part of a large mediaeval house. There is a history of Houghton Hall in manuscript form which I haven't read yet which might clear up the mystery, but in the meantime it would be nice to think that Saxton recorded the park just before its demise. The Houghton Hall estate used to be very large and it is not beyond the bounds of possibility that this is the site of a mediaeval deer-park. Royalty stayed quite often at Clare Castle when the castle was in its prime and this would be the nearest deer-park to the castle. Between 1230 and 1240 Henry III was resident at Clare more than once. There is documentary proof of this. In 1235, the king sent his huntsmen to Clare to take ten bucks in the park in readiness for the arrival of the court. Edward I, intending to hawk in the River Stour, ordered the sheriffs of Suffolk and Essex to keep the river free of other hawkers, and to ensure that the bridges in good repair. So it must be worth keeping an open mind about the possibility of a deer-park at Cavendish. We are on firmer ground in believing that the king of England used the Stour valley for hawking when resident at Clare Castle