Quick update from me - after just over 8 weeks from my initial request, I today received a re-payment onto my credit card for two cancelled BA flights booked through TravelUp.

The amount refunded was £266.61 short of the total paid (~£1600) as I had been told by TravelUp it would be.

I have now asked for a full breakdown of these costs. I was promised a 'invoice' for insurance purposes when I made my request for a refund, but have yet to see this.