Teresa,
They would probably have been married in the bride's parish - which was likely to have been in Birmingham (Aston, Erdington and Birches Green are all suburbs next to each other, just north of Birmingham City Centre).
I've looked at the familysearch website but can't see a marriage, so you'll probably have to search through the parish records for Birmingham, starting with churches in the areas of Aston etc. It could be a long job!
On the positive side, if you can spare the £7+ for each certificate, then you could get the birth records for some of the children. Civil Registration only started in July 1837, which would probably be too late for the marriage.
If you got a birth certificate for one of the children it would tell you the mothers maiden name and probably her address.
On
www.freebmd.org.uk I've found the following likely candidates:
December 1841 quarter
James Hayfield registered in Aston Vol 16 Page 206
March 1844 quarter
Eliza Hayfield registered in Aston Vol 16 Page 214
September 1848 quarter
Emma Hayfield registered in Aston Vol 16 Page 215
These look like the correct volume and page number to me, but you might want to check them before placing an order.
Certificates can be ordered directly from the General Register Office:
http://www.gro.gov.uk/gro/content/certificate/Regards,
Tim