at the end of the Second World War, returning servicemen underwent a 'demobilisation' process at various centres around the country. As part of this process of transitioning back into civilian life, they were issued with an outfit of civilian clothing. This included a new suit, which became known as a 'demob' (short for demobilisation) suit. Accordingly, the phrase has become synonymous with any suit that looks sufficiently mass-produced and out of style that no-one in their right mind would buy it themselves.
He goes to so few formal occassions, the last time he did he was wearing his demob suit.