It so happens, that I, too, joined HM Forces in 1942. Thus, your grandfather would have followed in the footsteps of thousands of men, who like me, were ordered to attend for medical examination etc at a former school for girls - the Recruitment Centre in Dover Street, Manchester. The premises are now part of Manchester University. It was there that it was prudent to visit one of the recruitment sections to see if one's civilian accomplishments would assist in joining the military unit preferred. (In my case there was a blockage at RAF flying schools on account of weather so air crew recruitment was being delayed. Reference to my uncle's RN service in the Great War ensured my eventual call-up to the FAA).
A photograph of the Dover Street building is available on the internet. Best regards. PhilipG.