My parents marriage certificate in 1938 shows my father as a widower but I have been unable to find a previous marriage or any records showing him as being married before. Would proof of first wife's death been required in 1938?
This is an extract from a response from the WDYTYA forum from a chap who is a registrar:
"The question the registrar would ask is essentially "have you ever been married before" and to be shown as a bachelor he must have answered "no". You can't really prove a negative, so there is no evidence he could be asked to produce to support that, it would be taken on his word (much as it is today).
"Had he answered "yes", then he would have had to produce evidence of divorce/death of his first wife."
That would appear to imply that your father said that he'd been previously married, that his first wife was deceased and that he produced some proof of that death, such as a death certificate. That does not mean that he had legally married his first wife, simply that he had a DC in her name.
There are, of course, lots of possible reasons why you can't find any marriage index, such as the marriage taking place outside England and Wales (or wherever you are), perhaps if he was serving abroad in some capacity.
(Thanks to AntonyM for the original and if there are incorrect bits above, it'll be my fault for miscopying.)
My answer quoted is essentially correct - but you would need to check what guidance was given to registrars (assuming it was a civil marriage), or clergy (for a church Marriage) on whether such evidence had to be physically checked at that time (it would be now). You might find such instructions in the Registrar General files at the National Archives (RG Series).