The two couples who assembled at Kew Palace on that day were Adelaide of Saxe-Meiningen and Prince William, Duke of Clarence, and Princess Victoria of Saxe-Coburg-Saalfeld and Prince Edward, Duke of Kent and Strathearn. The ceremony took place in the Queen's drawing room and though it was the first for Adelaide and William, Edward and Victoria had previously undertaken a Lutheran ceremony in Coburg on 29th May 1818.
Eventually Adelaide would become the Queen of the United Kingdom and Hanover, remaining devotedly with her husband until his death nineteen years later. For Victoria the marriage was a shorter affair, ended by her husband's death after just two years. Although she was never to hold the title herself, she was, of course mother to Queen Victoria, a monarchical legend.
Life in the Georgian Court, true tales of 18th century royalty, is available at the links below.