Are John Paddy Carstairs and Robert Hamer both film directors?
yes
Robert Hamer
Robert James Hamer (31 March 1911, Kidderminster, Worcestershire – 4 December 1963, London) was a British film director and screenwriter.
John Paddy Carstairs
John Paddy Carstairs (born John Keys, 11 May 1910 in London – 12 December 1970 in London) was a prolific British film director (1933–62) and television director (1962–64), usually of light-hearted subject matter.
 He was also a comic novelist and painter.
Sleeping Car to Trieste
Sleeping Car to Trieste is a 1948 British film directed by John Paddy Carstairs.
 The film is a remake of the 1932 film "Rome Express", with essentially the same characters and many of the same actors. Pink String and Sealing Wax
Pink String and Sealing Wax is a 1945 British drama film directed by Robert Hamer and starring Mervyn Johns, Googie Withers and Gordon Jackson.
 It is based on a play with the same name by Roland Pertwee.
 It was the first feature film Robert Hamer directed on his own. Meet Maxwell Archer
Meet Maxwell Archer is a 1940 British mystery film directed by John Paddy Carstairs and starring John Loder, Leueen MacGrath and Athole Stewart.
 The screenplay concerns a private detective who attempts to clear a man wrongly accused of murder.
 The film was based on the 1938 novel by Hugh Clevely.
 It was released in the U.S. in 1942 as Maxwell Archer, Detective. Anthony Nelson Keys
Anthony Nelson Keys (13 November 1911 - 19 March 1985) was a British film producer, best known of his work with Hammer Film Productions.
 His father was Nelson Keys and his brother John Paddy Carstairs. Dancing with Crime
Dancing with Crime is a 1947 British film noir film directed by John Paddy Carstairs, starring Richard Attenborough, Barry K. Barnes and Sheila Sim. Paris Plane
Paris Plane is a 1933 British crime film directed by John Paddy Carstairs  and starring John Loder, Molly Lamont and Allan Jeayes.
 It was made at Shepperton Studios as a quota quickie. A Yank in Ermine
A Yank in Ermine is a 1955 British comedy film starring Peter M. Thompson, Noelle Middleton, Harold Lloyd Jr. and Diana Decker, and featuring Jon Pertwee and Sid James.
 It was adapted by John Paddy Carstairs from his own novel "Solid!
 Said The Earl".
 The film includes the song "Honey, You Can't Love Two", sung by Decker and written by Eddie Pola and George Wyle. Holiday's End
Holiday's End is a 1937 British mystery film directed by John Paddy Carstairs and starring Sally Stewart, Rosalyn Boulter and Wally Patch.
 The film follows the arrival at boarding school of a boy king.