And the mystery is solved! I was looking through the 1939 England Register earlier. If you don't know, the register has the surname at the time it was taken but was kept updated up until the 1990s, meaning every time a woman got married they corrected the surname on the register.
Albert and Irene got married during the 1980s. In the same area of Yorkshire that the two got married in, in 1939, there was someone roughly Albert's age (a bit older) called Irene Oversby - the record was later updated to read "Irene Dowding" instead. I believe this person to be Albert's third wife as all the details about her - such as not having a middle name and living in the right area - match up with what I know about Albert's Irene.
The only mystery remaining now is why her marriage record reads "Dowding". There are no previous marriage records to suggest she married any other Dowdings, and the register only has "Dowding" and "Oversby", which suggests that Albert was her first husband. All I can presume is that something went wrong when they got married.