Okay your problem is that you have the live power coming into the switch - the red cable top right Common terminal - with, what we call strappers (red = L1 terminal and black = L2 terminal) or vice versa that link directly to the pull switch red = L1 and black = L2 terminals. The other red cable at the pull switch appears to go to the lamps live terminal at the ceiling rose.
Question though - in the picture of the ceiling rose it appears that the black cable is not actually connected to the neutral side of the lamp - is that correct or is it, I hope, an optical illusion?
If it is connected I will walk you through your options.
Yes apologies for the picture, just checked again and the black cable is connected to neutral.
You first of all need to remove the red link cable from the double gang switch – then move the top right red cable to the Common Terminal on the new switch.
Do the same for the hallway switch L1 (lower left red) put it in the L1 on the new switch.
This will give power solely to the hallway switch.
Then assuming that they are directly linked you can then disconnect the other red/black cable from the bedroom switch and the same at the pull switch.
Then assuming that the remaining single red cable at the pull switch goes to the ceiling rose – disconnect that at the pull switch and the ceiling rose.
Remove the pull switch.
Position the new switch where you want it and connect new Twin and Earth 1mm2 cable to it. Put the brown in Common and the blue (with brown sleeving) in L1 – sleeved earth to the back box.
Run the new cable into the loft with a lot of slack.
There are several ways to do the next bit.
I would suggest that find a nearby ceiling rose and run a T&E 1mm2 cable from it to the bedroom ceiling rose.
Connect the brown cable to the central three live loop terminals on both ceiling roses – do the same for the blue neutral loop terminals and the sleeved earth loop terminals.
Leave the old neutral cable alone.
Bring the switch cable up to the bedroom ceiling and connect the brown cable to one of the central three terminals with the other brown.
Connect the blue (with brown sleeving) to the ceiling rose lamps live terminal (brown) that runs down the cable to the light.