Can anyone explain how to wire up this 2-way switching?

The existing setup: A lounge with one ceiling light controlled by one
wall switch. Cables are twin & earth.

What I want to do is run a cable from the *ceiling rose* in the
lounge to an existing light switch in a hallway leading off from the
lounge.

I then want to replace the hall switch with a dual-gang switch. I want
one side of the new hall switch to control the hall light, and the
other side to control the lounge light. The original lounge switch
must behave as befo switching the lounge light on and off.

I'm guessing this is dead simple to do, but would be very grateful for
a link to the relevant wiring diagram, or alternatively, worded
instructions. Thank you in anticipation...

An alternative solution would be to run a cable from the lounge
ceiling rose to a second single-gang switch in the same room, so each
of teh two switches in teh room can then turn the light on and off.

Mike F