Duo's take some time to arrange, particularly among top prossies. So who is available is the big driver. As if KDD and Lizzy will be available on short notice. But they might.
Suggest you sort the London lists
by rating and start at the top (KDD, Adele, Khloe depending on nationality you choose) and phone them up and see if they have a friend and can fit you in.
Otherwise phone one of the popular agencies
. A bit more costly and more of a gamble but not easy on short notice.