OP, presumably your proposed flight to London still operated as well?
Aside from the fact that BA would only see a LHR-GVA flight, the fact remains that you therefore could still have taken the trip as booked and just done different things in Geneva. You, quite probably perfectly sensibly in your own eyes, made the choice to cancel - it was not imposed upon you.
In those circumstances, with the position on 3rd March being much less grave than it is now, it’s difficult to see why any airline should refund you.
I think the reality is that you’re going to have to accept the taxes back, or perhaps a voucher for future travel depending on when you booked.