Not all Belgian records have been fully indexed - there is no equivalent of freebmd. How much has been indexed depends on which area you're looking at. Liege (the city itself) is pretty well covered, but my lot from further south generally don't appear on databases. The name seems to be common in that area but not limited to it.
A lot *is* online as image sets rather than name-searchable databases, so if we can find anything that indicates a location we may be able to track his birth, and if he was married previously in Belgium there may be a marginal note on his birth referencing that marriage.
Another possible reason for not marrying until later is that because of the issues around Mary's divorce and the children born before/around the time of the divorce, they were just living together in London and telling people they were already married. By the time the divorce actually went through, they were already living as "Mr and Mrs" and it would have been a bit awkward to head down to church with kids in tow. Years later, they were then told they needed to show a marriage certificate for some official purpose, which resulted in a quick trip to the registrar's office.
