I am booked on a flight (DL) that lands into LHR T3 on Christmas Day. I have an onward flight, booked separately on a different airline (BA), that leaves from T5. When I booked these flights, my second flight was shown as departing from T3. In fact, upon checking, I can see that it departs T3 every day except Christmas Day. This must be due to consolidation of operations.

My question is how I can get from T3 to T5 on Christmas Day. I do not have checked baggage, however, I will have a gate-checked stroller that may or may not end up at the baggage claim carousel. If the stroller ends up at baggage claim, I will need to transfer landside. I have read that Heathrow Express operates its inter-terminal portion on Christmas Day. Can anyone verify? If not, any other options? Will cabs be available? If so, would they accept a 1-year-old without a car seat?

If my stroller is delivered on the jet bridge, and I have electronic boarding passes for the second flight, I would hope to be able to make an airside transfer. Can anyone verify that LHR buses offering terminal connections will run on Christmas Day?

I bought this itinerary based on the fact that
My flights were landing into and leaving out of T3 at the time of booking. Being well aware of Christmas Day travel issues in London and LHR on this holiday, I would have never booked had I known I would need a terminal transfer.

Thank you for any insights anyone can share. FWIW, I am a US citizen departing the US and my final destination is PRG.