Here are the entries for Minister in the 1851 Cambridgeshire Census and I think Edward is yours.
Cambridgeshire 1851 CensusHO 107/1760 429B
Hare & Hounds
CAMBRIDGE, St. Benedict Parish
John SWANN H M 27 Master Scavenger/3men & Publican Cambridge
Cecelea SWANN Wf M 24 Cambridge
Henry SWANN S 7 Scholar Cambridge
Cecelea SWANN D 5 Scholar Cambridge
Alfred SWANN S 3 Scholar Cambridge
Frederick SWANN S 1 Cambridge
Edward MINISTER? Lg M 66 Carpenter Cambridge
Robert GEE Lg Wdr 28 Scavenger Cambridge
William EMMEN Lg U 40 Scavenger Cambridge
George LOW Lg U 21 Scavenger Cambridge
Cambridgeshire 1851 CensusHO 107/1761 186A
Hildersham Hall
HILDERSHAM Parish
James RAYMOND H M 53 Gent ESS Wimbish
A M RAYMOND Wf M 47 MDX London
L A RAYMOND D U 17 Scholar at Home ESS Birdbrook
C A RAYMOND D 12 Scholar at Home ESS Birdbrook
R A RAYMOND D 8 Scholar at Home ESS Birdbrook
C G RAYMOND D 6 Scholar at Home ESS Birdbrook
William LEVELL Ser U 27 Footman SFK Stradishall
Ester MINISTER Ser U 41 Cook NFK Hadiscoe
Lucy HEFFER Ser U 27 House servt SFK Haverhill
Harriet FORDHAM Ser U 21 Kitchen servt ESS Hadstock
Elizabeth SUTTLE Ser U 23 Nurse SFK Clare
Caroline BARWASH Go U 28 Governess MDX London
Here is the only entry for Minister in the 1841 Cambs Census:
Cambridgeshire 1841 CensusHO107/85/16
7A / 7B
Parish Cambridge, St Andrew the Less
Dwelling 9 Blucher
Household
Edward MINISTER 45 Carpenter N Born
Elizabeth MINISTER 45 Y Born
James MINISTER 12 Y Born
Samuel MINISTER 10 Y Born
The following is from the Cambs Family History Society searchable indexes:
Cambs Baptism IndexYear Surname Forenames Age Abode Parents Parish
1827 MINISTER Amy - East Road of Edward & Elizabth. Camb. St.And.Ls.
1833 MINISTER Chas. M. - George St. s. of Edward & Elizth. Camb. St.And.Ls.
1825 MINISTER Elizabeth - East Road d. of Edward & Elizabth. Camb. St.And.Ls.
1829 MINISTER James - East Road of Edward & Elizabth. Camb. St.And.Ls
Cambs Burial IndexYear Surname Forenames Age Abode Condition Parish
1834 MINISTER Charles 1 George St. ----- Cambridge, St. Andrew the Less
I also found these on Free BMD
Deaths Mar 1843
MINISTER Elizabeth Cambridge 14 5
Deaths Jun 1866
Minister Edward 88 Cambridge 3b
313
Hope this helps!