I was traveling to Sudan in November as a tourist, but got my visa on my own. Am not Uk, but also for my passport it was waiting time like two weeks, but embassy in Vienna with a friendly phone call and personal visit arranged it in the same day. I saved on time and money. I think if you have embassy in London, call them, try to ask them, maybe it works. Otherwise for all those who are looking for visa info, i have compiled
ways to get visa for Sudan.