His birth registration:

Surname First name(s) District Vol Page
Births Mar 1843   (>99%)
Trotter Henry Barnet 6 474
________________

In the 1881 census his birth was written in the enumerators sheet, and below, as South Mimms, so this has to have been him and his family:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year Occupation Birth place

Henry Trotter Head Married Male 38 1843 Vicar Of St. Andrew The Less M.A. Hertfordshire
Eleanor C Trotter Wife Married Female 36 1845 -  London, Middlesex
Grace C Trotter Daughter Single Female 7 1874 Scholar  Greatham, Durham
Mary Hughes Servant Single Female 36 1845 Serv. Cook  Llansamlet, Glamorgan, Wales
Ann Wright Servant Single Female 34 1847 Serv. Ladies Maid  Lincolnshire
Martha J Wadsworth Servant Single Female 23 1858  Serv. Housemaid  Sheffield

Census details
First name(s) Henry
Last name Trotter
Relationship Head
Marital status Married
Gender Male
Age 38
Birth year 1843
Occupation Vicar Of St. Andrew The Less M.A.
Birth town -
Birth town as transcribed SOUTH MIMS
Birth county Hertfordshire
Birth county as transcribed HERTFORDSHIRE
Birth place England
House name Christ Church Vicarage
Street -
Town -
Parish Cambridge St Andrew the Less
County Cambridgeshire
Country England
Registration district Cambridge
Archive reference RG11
Piece number 1664
Folio 8
Page 10
Record set 1881 England, Wales & Scotland Census
_____________

In 1891 he was rector of Trowbridge with, apparently, still only the one daughter.
_____________

In 1901 he was living in Barnet, described as a Clergyman (Ch of England) and, apparently, without a parish to serve.  He and Eleanor still had but the one daughter.
_____________

In 1911 Eleanor Catherine Trotter was a widow with no sign of their daughter.
_____________

His death regisgtration:

Surname First name(s) Age District Vol Page
Deaths Mar 1910   (>99%)
Trotter Henry 67 Barnet 3a 173
_____________