What was the thinking was behind the black and white underside for the early Spitfires and Hurricans ?? Was it for recognition ??

This was for rapid recon purpose as at the time spitfire and hurricane were still few in squadron.Don't forget that at the time hawker hart and gloster gladiator were still in usebut were progressively replaced by modern fighter as spit and hurricane.
So to avoid confusion with modern bf109 they applied white and black markings underneath.
first half of complete underside and after phoneywar only wings were painted
Bat-21

The main reason was, as you say for recognition purposes. It was ACM Dowding who pressed for a two colour underside, he asked for half silver dope and half black. [He also wanted the upper surfaces to be completely green for better camouflage on the grass airstrips]. In 1938 the air ministry decided on white/black undersides. On 6 June 1940 it was changed to duck egg green after reports from pilots in combat stated it put them at a disadvantage. Strangely from November 40 to April 41 they introduced an all black paint for the underside of the port wing. It seems the thinking was it is better for everyone to spot RAF aircraft than to have our own aircraft attacking each other in error.