Abduction serial killers often choose to travel a considerable distance in order to deposit their victim.
It's not just the act of killing that they enjoy, but rather the process of abducting, controlling, and spending some time with their victim before they kill them; all the while enabling time for the victim to feel fearful of their life, and even give them false hope that they will be spared.
Abduction and Deposition sites are often far enough away from each other for the police to have a tougher time in tracing the culprit.
By a killer travelling across jurisdictional boundaries, it makes the job of the police all that bit harder.
So one would expect that the man who abducted SL, is likely to have travelled outside of the local buffer zone in which the victim was taken.
It's important to differentiate between the abduction site, the kill site, and the deposition site, as they can all be vastly different in terms of geographical location.
If the killer did drive SL out of London then the obvious choice from Fulham, would be west via the M4...towards Bristol.
But the killer may have taken her to a lock up/bolt hole first, and then drove her to the deposition site later.