Peter Townsend does not specify what disease he is suffering from. The real-life Peter Townsend died from stomach and colon cancer in 1995 at age 80.
In reality, Princess Margaret's episode of Desert Island Discs was broadcast in January 1981, and did not include anything by Hoagy Carmichael. Her choices did not seem to include anything that might be considered romantic or evocative.
The real Guildhall in the City of London is a restored medieval building, both inside and out. The location setting, Greenwich Old Royal Naval College, is a neo-classical (Wren) building and bears no resemblance at all to the original.
Princess Margaret, played by Lesley Manville meets her former lover Peter Townsend, played by Timothy Dalton. Timothy Dalton is well known for having played James Bond in The Living Daylights (1987) and Licence to Kill (1989). Coincidently Lesley Manville has performed in Fleming (2014), portraying Evelyn Fleming, the mother of Ian Fleming who is famous for being the author of the James Bond book series.