Skylon does have the advantage of burning atmospheric oxygen at low altitudes, meaning it would have a significantly higher payload fraction than the Falcon 9.
Plus, payload fraction is another thing like SSTO, horizontal takeoff, novel heat shields, and all the rest that are cool but just don't matter except for how they affect the end result. All that matters in the end is how much you can launch, and how much it costs.
That's the critical point. Skylon is still vaporware, and they've really assumed the best case in published numbers.
So, afterwards, it needs another 8000 m/s Δv on rocket engines to reach LEO.
Skylon is a neat trick, but it's not magical.