If circumstances and insanity demand, and in a car with a co-driver, it's possible to do London to Aqaba in 4 days without too much trouble.
It's not a huge amount of fun obviously, and on a bike would be a bit of a challenge.
Our itinerary last month could have been
Weds 23:00 My brother leaves the pub and heads for the channel.
Thurs 03:00ish Takes the tunnel, then France, Bel, Lux, Germany, Austria
Thurs 21:00 Picks me up at Vienna airport, then Hun, Serb,
Fri 06:00 Hit Bulgaria ( with abit of research, might have avoided Bulg)
Fri 18:00 Hit Turkey (after a few hours debating insurance with Bulg Police)
Sat 04:00 Pass Ankora
Sat 15:00 Hit Syria
Sat 21:00 Hotel in Hamma
Sun 07:00 Leave Hamma
Sun 12:00 Hit Jordan
Sun 20:00 Aqaba
Times are approx obviously, and we stopped for food, deisel and a couple of knaps when neither of us could manage any more.
Actually we took a day each for diversions to Palmyra and Petra, but didn't have time for anything else.
4 days is definitely do-able in a car, and 1-2 days Syria/Jordan is also quite straight forward.