Never going to happen. The slot waiver is likely to be extended to this winter but even if it wasn’t, this route would be way down the list.
It would have to be flown by the E170/190 as that’s the only aircraft BA have that can serve LCY.
LCY also has a lot of duplicate routes to LHR (EDI/GLA/AMS) so there wont be any connecting traffic who arrive at LCY and want to transfer onto long haul. A better alternative would be LHR-LGW, but even that had near zero chance of starting. There are barley any routes left at LGW and there just isn’t the demand right now.
If BA had to slot sit, they would up frequencies to existing destinations (we’d see a 15:15 and 15:30 to EDI for example). I’d imagine some new Euro routes would start at 3/4 daily to block some slots too.