I've been several times on BA's shuttle flights London - Glasgow and London - Edinburgh. Planes were B737 and B757. Flight duration about 50 mins.
Also, London - Glasgow by AirUK on BAe147 - around 1 hour and Fokker 100.
But the shortest was on a Aeroflot's Tu-154B-2 with flight time of 40 mins. Yakutsk - Mirniy (two cities in Siberia).