Thank you all for the responses. I just checked the 709 ZRH-LHR on ba.com and it says the flight is cancelled so I've lost hope for that flight.

I think the best way forward is to head to the airport as early as possible tomorrow to try to get on the LX 316 ZRH-LHR or LX 460 ZRH-LCY.

Before I do this - a couple questions please:

1) Just to confirm, I can indeed try to rebook on LX as my original BA 709 was cancelled, even though I have been alternatively booked on BA 713 (which doesn't meet my timing requirements)

2) If LX 316 ZRH-LHR is full, could I try to persuade the LX staff to book me on LX 460 which goes into LCY? is this even possible as I know there are no partner agreements with LX/BA. Not sure what I should be expecting from LX here.

Thanks in advance everyone for your help with this - unfortunately BA hasn't been any help!