BS1363 plugs have square pins so that they're deliberately incompatible with the previous UK plugs - the pre-1947 system was not safe, and BS1363 was a successful attempt to fix its many problems. The reason why the plug is mechanically incompatible is because the UK adopted a fuse-in-plug system - Continental plugs are fused at the distribution board, which means if a piece of equipment fitted with a continental plug were to short-circuit, it would only trip when it hit the ring-main's guard fuse limit, which is 32 Amps.
Actually, that's not quite true, as most electronic equipment had a fuse-in-device, rendering the UK socket fuse redundant (just as well: 13 Amps is a huge amount of current in Electronics; most equipment is fitted with 5 Amp fuses or lower)
( In one concession the L/N holes of a UK socket will accept a two-pin "Europlug" (a.k.a. "shaver plug") if you push the earth shutter with the end of a Bic biro - this was allowed because that kind of two-pole plug is used only for loads under 3 Amps.)
The UK system's insistence on earth provision is its best feature. However, earthing is not as much of a safety bonus these days, as the vast majority of domestic electrical equipment is double-insulated Class II (a classification that didn't exist in 1947), and thus has no connection on the earth pin.
Ireland uses the same plug type of the UK, largely because it was a good design, but also for pragmatic reasons: most trade was with the UK, and it allowed compatibility with Northern Ireland (the Island of Ireland has always been a single electrical grid). Our regulations don't permit ring mains, though: sockets are wired on single-ended spurs.
In one odd hangover of colonialism, Singapore, Malta, Cyprus and Hong Kong* also use these plugs, which was always handy for people doing a bit of consumer-electronics shopping on their way home from Australia. (Especially back in the days of analogue TV, as HK also used the same PAL-I colour system as the UK)
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* but only Hong Kong: in mainland China, domestic installations use whatever was in the first box the electrician pulled from his van.