As of early June 2023, satellite to satellite comms are not enabled on Starlink, which means currently packets hit the satellite and then return to a ground station for further on transmission. The long distance latency improvement you seek can only work if you cut out the ground section entirely.
And Probably Never
NYC to London one-way time is about 28ms. You can double check this with some simple math:
5,585 km / (0.66*300,000 km/s) = 0.028s
Where the 5,585km is the NYC to London distance and fiber transmissions occur at roughly 66% the speed of light in vacuum.
Starlink orbits at about 550km, which means we need to add 1,100km to the distance for the up and down legs - but we use the full speed of light so that helps.
6,700 km / 300,000 km/s = 0.022s
This looks good for Starlink, but there's also hop latency, and the likelihood of more hops.
Each router will add around 5ms of latency. The traditional fiber scenario has one router hop - the one at the remote side. The Starlink version will have 5: one on each satellite in each direction, and one at the ground on the remote side. So the round trip is now 28x2 + 5 vs 22x2 + 5 + 5 + 5 + 5 + 5 or 61ms for fiber and 69ms for Starlink. Already a problem for Starlink.
This is also a problem. It is unlikely that Starlink will transmit from directly over NYC to directly over London. Rather, it is likely that multiple hops will occur in space as the curvature of the Earth and the presence of atmosphere prevent a direct laser link across 6,000km from LEO.
Each hop will add 10ms per round trip, and additional transmission distance (we're not moving in a straight line any more - instead we're zig-zagging)
Router Improvements and Bottom Line
It's possible to drive the router delay down (obviously not all the way to zero, but lower). So maybe the router delay can be driven low enough that it is negligible compared to the extra travel distance, but I'm not going to bet on it. If multiple satellite hops are required, the extra distance and extra router delay will both be meaningful penalties.
Starlink will probably never beat fiber for transatlantic communications latency.