Hi Sheila
I think it is probably unwise to assume that the couple were married in Northampton (not sure what the Northampton connection is!) or Cambridge. Charles was from Eltham in Kent (now south east London) so they could have met and married there, or in Nottingham (where they were in 1881 as man and wife) or, frankly, anywhere!
Your best bet is to get Kate's birth certificate. This will give you Elizabeth's maiden name, which should make the marriage much easier to find. Here is the reference from FreeBMD:
Births Dec 1884
Martin Kate Nottingham 7b 315
You can get the certificate direct from
www.gro.gov.uk for £9.25 including postage.
In case you don't already have them, here are the census entries for the family in 1881:
Charles Martin 23 Head Corn Miller's Labourer born Kent
Elizabeth Martin 21 Wife born Cambridge
Address: 5 Poplar Square, Nottingham, Notts
Ref: RG11; Piece: 3352; Folio: 80; Page: 26
and in 1891:
Charles Martin 34 Head General Labourer born Eltham, Kent
Elizabeth Martin 29 Wife born March, Cambridgeshire
Charles Martin 9 Son Scholar born Nottingham, Notts
Kate Martin 6 daughter Scholar born Nottingham, Notts
Harry Martin 3 son born Nottingham, Notts
William Martin 1 month son born Nottingham, Notts
Address: 25 Billingsgate Street, Greenwich
Ref: RG12; Piece: 508; Folio: 10; Page: 14;