Hi Val
The "brick wall" you refer to is far from unusual. In fact, it is something every UK researcher has to deal with. For many people, getting back to the beginning of the 19th century can be achieved in a quite straightforward fashion, using the standard method of census information and civil registration certificates which can generally be combined to provide a reasonably reliable paper trail of evidence. But that trail goes suddenly cold when you no longer have a census to check and civil registration certificates have to be substituted by parish registers which do not (in the vast majority of cases) provide data about other members of the family.
Your research will slow down from now on and your methodology will change. Rather than plotting your tree in a tidy, linear manner, you will need to assemble smaller pieces of more speculative evidence which will need more thoughtful evaluation. Your chances of success from now on are less predictable and will be affected by a number of factors which include:
a. The relative commonness of your family's names and/or occupations
b. The degree to which they moved around the area/country
c. Their economic situation - the better off they were the more likely it is that their names will be recorded in official documents. Wills in particular are a gold mine as they often refer to a large number of individuals and relationships.
d. Your commitment in terms of time and money. You will almost certainly need to consult sources that are not available online.
At the current point of your quest, a good strategy is to try and identify siblings of the couple in question. Your pair married in 1834 but they may have had a younger brother or sister who married after 1 July 1837 whose marriage certificate will give you the fathers' information you seek.
I hope this is helpful
Caroline