Almost, but not quite. There was not and is still no unified procedure for having a missing person declared dead in England or Wales - separate courts have to be approached to deal with each particular aspect of the problem. The High Court can dissolve a marriage on the basis of presumed death but, as you say, this would be complicated and costly - probably more so in the early 20th century than a divorce, for which there were almost certainly grounds.
However, presumption of death - on the basis that a person had been gone heaven knows where for 7 years or more and no one who might have been expected to hear from them had done so - was considered an unrebuttable defence against bigamy. So if a person who genuinely believed that their spouse was dead remarried in that belief (and declared themselves to be widowed), successful prosecution was very unlikely.
Or they could just have fibbed and kept their fingers crossed!