Bobbsy,
I also live in London, bike parked off street chained to the floor.
I swapped my 1200 GS for a new 650 V Strom last June.
Was amazed when my insurers, Devitt, would n't insure it.
I thought the smaller bike would be less of a problem.
Bennetts sorted me out & the premium was about £50 less than the GS fully comp.
Are you under 25 ?
My old bandit was insured through devitt, they weren't able to offer a renewal quote as the underwriter has changed their policy and would no longer insure bikes in London.