Wasn't aware of brick type being a factor in the efficacy of cavity wall insulation. I also thought that London bricks were pretty hard, and think that's what I have here. I've always been in favour of this since my first house in '75, but couldn't then because only the ground floor was cavitied (odd !). I then made a horrendous error in having Rentokil down to fill the walls in my 1870 detached multi-room house with 3 walls thick in the servants' quarters. Rentokil had to get another lorry load of rockwool sent down (to Ramsgate) from London, because the cavities were over 2" wide. Unfortunately, debris had built up or simply been deposited by the builders, which breached the few air-bricks and engineering brick DPC. Many dry-rot years later........!
I had my next 1964 suspended floor house filled, with added air-bricks, which was okay, and my current 1962 house with concrete floors; again, no prob's 21 years later. Concrete floors, nowt to rot; suspended, could be a problem unless suitably ventilated sub-floor. Obv. you're concerned about the insulation getting wet; maybe rusting the tie-bars (as happened on a neighbour's property)? I do believe it works, but side-effects can be a worse problem than cold. Interior Celotex is a good if laborious solution i.m.o.but you do need interior space not to compromise capacity.