*** Not quite free, but £2 which is a lot less than the usual price (£7) ***
One of the city’s most famous landmarks, Norwich Castle was built by the Normans as a Royal Palace 900 years ago. Now a museum and art gallery, it is home to some of the most outstanding collections of fine art, archaeology and natural history.
Norwich Castle does a "Pop in for a £2" deal (used to be "pop in for a pound" up until recently, *sigh*)an hour before closing everyday, and also between 12-1pm weekdays during school term.
This would work out as:
Until 1st July - Mon - Sun 3.30 - 4.30 pm
1st July - 30 September - Mon - Sun 4-5 pm
More info from website
Read my thoughts about "not quite free" posts here