Drywall – 1920 UK London House – How should I internal insulate

There are a few possibilities; without knowing more about the layout of the house makes it harder to say for sure.

The internal wall in the garage might be constructed in normal blocks for fire performance reasons. (Without looking, I'm not sure about the fire performance of thermal/lighweight blocks). Also, normal blocks might have been used for structural reasons - for example if the wall is load-bearing (normal blocks generally have a higher compressive strength than thermal/lightweight blocks).

Likewise with the bathroom and en suite - there might be a difference for structural reasons.

Or there might be no firm reason for the difference at all, other than the builders using what they had available - it's not unusual for builders to use what they have as long as it meets any specific requirements for the particular element of the structure.

Condensation is definitely a concern in colder weather. If you create a thermal break that isn't properly sealed against air leakage, warm air from the house will seep behind the walls, bringing lots and lots of moisture with it. Meanwhile the bricks, which are now insulated, are going to be very very cold, and when warm air gets cold it lets go of its moisture - and thus we get condensation.

That condensation would then get trapped inside the walls - and long before you have a problem with brick deterioration you're going to have mold issues that lead to health issues.

The best thing to do to prevent this is to insulate with a substance that also serves as a vapor barrier, which will prevent any air (and thus any moisture) from leaking into the closed cavity. The best product for this IMO is spray foam insulation, because it fills in all the nooks and crannies and IS the vapor barrier.

Alternatively, you could use fiberglass and cover it over with plastic to form a vapor barrier, and this can work IF you properly seal it all the way around the edges, seams and any holes that occur.

Either approach, however, is going to require you to sacrifice living space, as for a proper thermal break you're going to probably want at least 4" of insulation.

Now - with regard to insulating your spare rooms. Don't insulate your interior walls. Put proper insulation in the external walls of those rooms, so that they don't lose heat to the outside. Yes you will be heating them, but if they're properly insulated they're not going to cost much to heat and there are numerous other concerns with turning an inside room into a "cold" room - it's a finished space, after all, and you don't want to risk damaging that by letting it be freezing cold in there.