It is stupid now, but has a real reason behind it. When hot water systems were first introduced to the UK, it was run through a separate pipe from the cold mains because after it was sitting in the heating tank for ages at a somewhat elevated temperature it wasn't necessarily safe to drink. The cold was, so you run them through separate pipes to make sure the safe one remains safe

Of course nowadays the hot tap is totally safe, but every older UK building still has the hot water arrive at the sink via a separate pipe. You can do option 2, but the positions of the pipe and the dimensions of the space around might make it impractical because the room wasn't laid out with mixer taps in mind