Mid-January I'll be transferring from an inbound SK flight arriving at Terminal 3 at 15:55 to a BA flight leaving Terminal 5 at 18:40, so theoretically a 2hrs 45 mins layover. They're on two separate itineraries. BA flight is Club World. I can arrange it so that I'll have no check-in luggage but will have a small kid (2 years) in tow.

I assume that the quickest way in this scenario is airside transfer but how long will this take and is there any sort of Fast Track if you have a BA CW ticket outbound again? Would I be able to make it with luggage and landside transfer?

Not knowing what January weather will bring in terms of delays and cancellations I'm sort of nervous about even such ample connection time.