As you already know they married in 1810 you may already have this Record. No parents names I'm afraid. This can be viewed in the Members Area Section of this website

record_id 7125
Entry Number 680
Year 1810
Month Jul
Day 2
Groom Surname CUTTER
Groom Forename(s) Thomas
Groom Age at Marriage [not
Groom condition [not stated]
Groom Rank or Profession [not stated]
Groom Residence of this parish
Groom Father's Surname [not stated]
Groom Father's Forename(s) [not stated]
Groom Father's Rank or Profession [not stated]
Bride Surname MORGAN
Bride Forename(s) Susanna
Bride Age at Marriage [not
Bride Condition [not stated]
Bride Rank or Profession [not stated]
Bride Residence of this parish
Bride Father's Surname [not stated]
Bride Father's Forename(s) [not stated]
Bride Father's Rank or Profession [not stated]
Licence or Banns Banns
Date of banns [no register fou
Signature or Mark Both mark
Witness 1 William Jones
Witness 2 Rich[ar]d Terrett
Other witnesses
Officiating Minister William Prosser
Event type Marriage
Memoranda
Transcriber's Notes
Register Reference P138 IN 1/7
Page No 71
Parish/Chapel English Bicknor
Soundex Groom C360
Soundex Bride M625

These BMD's may well link in....

--------------------------------
JOHN CUTTER
---------------------------------
Event(s):
Birth:
Christening: 08 OCT 1786 Newland, Gloucester, England
-------------------------------
Parents:
Mother: ELIZATH CUTTER
------------------------------------------------------------
Messages:
Extracted birth or christening record for the locality listed in the record.
The source records are usually arranged chronologically by the birth or christening date.
--------------------------------------------------------------
Source Information:
Batch No.: Dates: Source Call No.: Type: Printout Call No.: Type:
C036202 1560 - 1565 0423272 Film 6911882 Film
C036202 1583 - 1812 0425476 Film NONE
Sheet: 00

ELIZABETH CUTTER
------------------------------------------
Marriages:
Spouse: RICHARD POWELL
Marriage: 18 SEP 1784 English Bicknor, Gloucester, England
--------------------------------
Messages:
Extracted marriage record for locality listed in the record.
The source records are usually arranged chronologically by the marriage date.
------------------------------------
Source Information:
Batch No.: Dates: Source Call No.: Type: Printout Call No.: Type:
M036081 1754 - 1844 0855609 Film 6905381 Film
Sheet: 00

ANN CUTTER
---------------
Marriages:
Spouse: GEORGE RICHARDS
Marriage: 27 DEC 1760 English Bicknor, Gloucester, England
--------------------------
Messages:
Extracted marriage record for locality listed in the record.
The source records are usually arranged chronologically by the marriage date.
---------------------------------------
Source Information:
Batch No.: Dates: Source Call No.: Type: Printout Call No.: Type:
M036081 1754 - 1844 0855609 Film 6905381 Film
Sheet: 00

RICHARD CUTTER
--------------------------------------------------
Marriages:
Spouse: MARY JAMES
Marriage: 12 AUG 1756 Goodrich, Hereford, England
-------------------------------------------------
Messages:
Extracted marriage record for locality listed in the record.
The source records are usually arranged chronologically by the marriage date.
-------------------------------------------
Source Information:
Batch No.: Dates: Source Call No.: Type: Printout Call No.: Type:
M145921 1661 - 1843 0992150 Film NONE
Sheet:

-------------------------------------------------


HANNAH CUTTER
------------------------------------
Event(s):
Birth:
Christening: 10 DEC 1758 Goodrich, Hereford, England
---------------------------------------------
Parents:
Father: RICHARD CUTTER
Mother: MARY
----------------------------------------------------------
Source Information:
Batch No.: Dates: Source Call No.: Type: Printout Call No.: Type:
C145921 1661 - 1874 0992150 Film NONE
Sheet:

MARY CUTTER
---------------------------------------
Event(s):
Birth:
Christening: 30 JUN 1771 Goodrich, Hereford, England
---------------------------------------------
Parents:
Father: RICHARD CUTTER
Mother: MARY
----------------------------------------------------
Source Information:
Batch No.: Dates: Source Call No.: Type: Printout Call No.: Type:
C145921 1661 - 1874 0992150 Film NONE
Sheet:

1841 Coldwell - opposite Symonds Yat
Thomas Cutter abt 1781 Herefordshire, England Goodrich Herefordshire Hoop Maker
Hannah Cutter abt 1786 Herefordshire, England Goodrich Herefordshire
Alfred Cutter abt 1836 Herefordshire, England Goodrich Herefordshire
James Cutter abt 1831 Herefordshire, England Goodrich Herefordshire
John Cutter abt 1826 Herefordshire, England Goodrich Herefordshire
Thos Cutter abt 1821 Herefordshire, England Goodrich Herefordshire

http://www.old-maps.co.uk/
coords 357102,216299

possible Death entry
Name: Thomas Cutter
Year of Registration: 1847
Quarter of Registration: Jan-Feb-Mar
District: Ross
County: Gloucestershire, Herefordshire, Hereford and Worcester
Volume: 26
Page: 226

1851
Hannah Cutter abt 1786 Bicknor, Gloucestershire, England Head Huntsham Herefordshire
William Cutter abt 1825 Goodrich, Herefordshire, England Son Huntsham Herefordshire
Alfred Cutter abt 1835 Ragland, Monmouthshire, Wales Grandson Huntsham Herefordshire

and other CUTTER Families nearby

1841 Goodrich
Georg Cutter abt 1785 Goodrich Herefordshire ag Lab
Ann Cutter abt 1792 Herefordshire, England Goodrich Herefordshire
Caroline Cutter abt 1826 Herefordshire, England Goodrich Herefordshire
Daniel Cutter abt 1821 Herefordshire, England Goodrich Herefordshire
Eliza Cutter abt 1832 Herefordshire, England Goodrich Herefordshire
Sarah Cutter abt 1829 Herefordshire, England Goodrich Herefordshire

1841 Joyford
John Cutter abt 1791 Gloucestershire, England Bicknor English Gloucestershire Ag Lab
Phebe Cutter abt 1791 Gloucestershire, England Bicknor English Gloucestershire
Hannah Cutter abt 1821 Gloucestershire, England Bicknor English Gloucestershire
Milson Cutter abt 1828 Gloucestershire, England Bicknor English Gloucestershire

1841 Ellwood
Isaac Cutter abt 1791 Gloucestershire, England Dean Forest Gloucestershire Quarry man
Mary Cutter abt 1791 Gloucestershire, England Dean Forest Gloucestershire
Cilia Cutter abt 1826 Gloucestershire, England Dean Forest Gloucestershire
Isaac Cutter abt 1821 Gloucestershire, England Dean Forest Gloucestershire
James Cutter abt 1832 Gloucestershire, England Dean Forest Gloucestershire
Thomas Cutter abt 1816 Gloucestershire, England Dean Forest Gloucestershire

1841 Lane End
William Philips abt 1806 Dean Forest Gloucestershire Wheelwright
Ann Philips abt 1832 Dean Forest Gloucestershire
Sophia Philips abt 1816 Gloucestershire, England Dean Forest Gloucestershire
Eliza Cutter abt 1840 Gloucestershire, England Dean Forest Gloucestershire
George Cutter abt 1837 Gloucestershire, England Dean Forest Gloucestershire
Henry Cutter abt 1833 Gloucestershire, England Dean Forest Gloucestershire

I'm sorry this comes so long after you posted the message but I've only just found it. There was a family of Cutter's living in Bicknor Street, English Bicknor right up until the late 1960's early 1970's.

I was given the date of 15 Dec 1786 in the church of E Bricknor for the baptism of Thomas CUTTER who married Susanna MORGAN in 1810 at Eng Bicknor, I cannot find it in the Parish Records

Year: 1810
Month: Jul
Day: 2
Grooms_Surname: CUTTER
Grooms_Forenames: Thomas
Grooms_Age:
Groom_Condition:
Grooms_Occupation:
Grooms_Residence: of this parish
Grooms_Fathers_Surname:
Grooms_Fathers_Forenames:
Grooms_Fathers_Occupation:
Brides_Surname: MORGAN
Brides_Forenames: Susanna
Brides_Age:
Brides_Condition:
Brides_Occupation:
Brides_Residence: of this parish
Brides_Fathers_Surname:
Brides_Fathers_Forenames:
Brides_Fathers_Occupation:
Licence_or_Banns: Banns
Date_of_Banns: no register found
Signature_or_Mark: Both mark
Witness_1: William Jones
Witness_2: Richard Terrett
Other_Witnesses:
Officiating_Minister: William Prosser
Event: Marriage
Memoranda:
Notes:
Register_Reference: P138 IN 1/7
Page_Number: 71
Parish_Chapel: English Bicknor

Fred Cutter