I know very little about rocket launches, but one thing I thought I understood was that launches want to take off from as close to the equator as possible, which southwest England is not. Was there something special about the payload or this launch site? Or is this the launch equivalent of fighting with one arm tied behind your back? //

The optimal launch site for a given launch is at the same latitude as that launch's orbit's inclination. Depending on available downrange space, a particular site can also launch to orbits higher than its latitude, but never lower (without doglegs, which I'm going to ignore for the rest of this comment). So a low-latitude site is better in general since it makes more orbits possible, but it's not the best site for all orbits.

This launch by Virgin Orbit is going to polar orbit, which is extremely high-latitude. So it's possible from basically any launch site, and in fact is slightly better from high-latitude sites. //

It depends on your target orbit.
If you're shooting for an equatorial orbit, launching from near the equator gives you a boost from the Earth's speed of rotation, and saves you from needing to build a wasteful dog-leg or plane-change manoeuvre into the flight plan. This saves fuel and therefore lets you fly a bigger spacecraft with the same launch vehicle.
If you're shooting for some types of polar orbit, then the Earth's rotation is just an annoying thing you need to cancel out, so launching from a high latitude is more efficient.
The point of Virgin Orbit's approach is that you can launch the airplane from any convenient place with the right infrastructure, and fly to the best latitude for the type of mission you're doing that day before you light up the rocket, and you have good odds of bring able to launch without the weather problems that can cause delays when you're constrained to one fixed site.