Hi, Stephen,
Afraid I'm not related to the Shutt family but have come across Robert Shutt, Supervisor of Excise at Poole, Dorset, in a convoluted search of my own.
He married Elizabeth Barker by licence at Catterick, North Yorkshire, 17 Oct 1765.
See the will of Christopher Barker dated 27 July 1779. This is listed on Ancestry's Probate Records as Christopher Barker, probate, Catterick, 1780, gent, will with codicil, Ref No. RD/AP1/146/156.
Robert & Elizabeth had a daughter, Mary, born in York, 1767, died 18 July 1786.
The National Archives probably has his records as an Exciseman. If they are as good as those for Customs officers, you could learn a lot.
Hope some of this helps.
R