Welcome to rootschat
Edward was baptised at Mundesley (freereg)
Birth 02 Dec 1841
Baptism 30 Dec 1841
Edward Montague Martin
Parents Thomas & Elizabeth
Father's occupation Solicitor
I notice on the BT's that the Rector was Robert Steele, was he related to Elizabeth

You have the death for Thomas as 1843/5? Where does his year of birth come from

There is a burial in Kensal Green 26 March 1846 for a Thomas Martin age 29, his abode was 3 South Square, Grays Inn, St Andrews, Holborn. This area in 1841 was the residence of many solicitors/barristers (H0107/729 bk 5 folio 5 page 2 ).
This is the death registration index for him
MARTIN, THOMAS age 29
1846 March Quarter in HOLBORN UNION Volume 02 Page 87