I'd have said that the Blue Suit with a collar the same would have been 'Night Clothing' - usually the "No.2" suit of serge with no cotton collar worn. The 'jumper' underneath would have been a sea jersey - winter clothing which was worn instead of the white front.
The branch badge would indeed have been that of a Radio Operator, but called 'Telegraphist' in those days, in fact up until the late 1950s.
Cap Tallies - 'HMS' and 'HM Submarines' - the explanation by 'PartTimer' seems fine to me, though I'm sure there were economic reasons as well. There was also a great deal of personnel movement between ships as well and with the best tallies being made of gold (OK, golden) wire, I'm sure it saved some money. The use by submariners of HM Submarines was originally more due to the great deal of movement of personnel between different boats, e.g. from 'Spare Crews' etc, at short notice, though this has reduced now (most of the 'Diesel' Squadrons could comprise up to 10 boats). It was also the submariner's mean of identifying himself as a member of the elite, when in working dress - the 'badge' came a bit later and was only worn in square rig anyway.