I only know of 2 in this area - STM in Henfield, West Sussex which we use and are fine for what we want to do ie a pig occasionally or a couple of sheep (also do cattle) and Laverstoke Park near Basinstoke which are probably nearer to you, but too far from us so can't give an opinion.
I find it hard to believe that there is nothing in London, but lost the will to live whilst searching!