Going round Shute Barton is a slightly surreal experience as it's a National Trust holiday cottage, which they open to members of the public four times a year for guided tours. See the National Trust's official site, detailed below, for opening times, admission prices, etc.
What you see today is only the servants' quarters of what was once a very grand house. A painting in one of the bedrooms shows the house as it may have looked shortly after it was completed in the mid 15th century.
The rest of the house was demolished when Sir John William de la Pole bought the estate in 1787. He built a new Shute House a quarter of a mile further along the drive, which is not open to the public.