corporate-wage-slave

If I may be rather blunt (and I'm still on my first coffee of the day) if I was working in a Contact Centre and hearing the above, my assumption would be that you cancelled your own booking by accident, having for whatever reason ended up in the "Cancellation options for this booking", and rather than stopping at that point, ploughing on for a refund.

However! When I went into BA.com to check my answer, strangely enough it came to life with the last thing that I was doing (full website, Internet Explorer), which in my case was a harmless fare check. It would normally come up with the front screen. BA is perpetually making small changes to their online products, using Agile, so new things pop up quite regularly, and mostly they are steps forward, sometimes they are a step backwards - these often get reversed quickly.

Now this is effectively 2 anecdotes rather than anything confirmed, but it is the case that BA's website has multiple weaknesses. Also if you are making an SDC / FCOD then you can do that online most of the time. Furthermore there is a short period of time - minutes not hours - where the booking may look a bit of a mess (particularly on the App) between the change being made and the ticket being fully revalidated. If the screen had shown a refund, which definitely doesn't apply in this case, you should have stopped, logged out, got a coffee, started again.

In your position I would buy a new ticket, or use Avios (there is a ton of availability from LHR, LCY and LGW for your dates, incidentally), then write to Customer Relations and explain that you did not willingly cancel this booking, that you immediately contacted BA, and that you don't think this should have happened. If Customer Relations declines to rectify this by refunding the Avios booking, which would not surprise me, then you do have legal remedies thereafter, if you feel very strongly that the fault was not at your end.