Henry in bed in hut (5)
I believe the answer is:
shack
'hut' is the definition.
('shack' can be a synonym of 'hut')
'henry in bed' is the wordplay.
'henry' becomes 'h' ('H' can be a synonym of 'henry').
'in' indicates putting letters inside.
'bed' becomes 'sack' (e.g. 'in the sack').
'h' inserted within 'sack' is 'SHACK'.
'in' is the link.
(Other definitions for shack that I've seen before include "basic accommodation" , "Rough dwelling" , "grim lodgings" , "Hovel" , "Rough hut or cabin" .)