Dianne,
I presume you have searched FreeBMD and found nothing, as I just did. It looks as if they have transcribed all records between 1866 and 1871 which is the most likely date range for the marriage, although they could have been living together without benefit of marriage in 1871.
The only thing I can suggest is to try parish registers from 1866 on, (in case Rachel was married at a very young age, unlikely), for the parishes of both parties. You will need Powys Record Office, (
http://archives.powys.gov.uk/), for Brecon, and Gwent Record Office, (
http://www.llgc.org.uk/cac/cac0004.htm), for Monmouth.
It is also possible that the marriage, if it happened, is recorded in the local registar's records but was missed from the GRO index. The record offices will be able to advise if it is possible to search their records or if you have to provide the date of the marriage in order to get a certificate. Most annoying when this is required!!!
Unfortunately there is no local indexing project underway on
http://www.ukbmd.org.uk/index.php for the counties you are interested in.
Good luck with your search.
Viv Pyner
Co-ordinator for Monmouth 1871 for FreeCEN
Free census indexes for everyone
http://freecen.rootsweb.com/