The Duchess of Argyll claimed that the divorce had made her all but penniless, and she lived the remainder of her life in relative obscurity, dying in 1993 at the age of 81. There is some cause to doubt her claims of poverty, although the cost of the divorce and her subsequent social ostracism certainly hit her hard.
The Duke of Argyll re-married only a few weeks after the divorce was finalized, as the captions at the end of the episode state. This marriage (his fourth) lasted until his death in 1973.