Not in SE1 but nearish - I recently had some very delicate/ finely detailed butterflies done on my back by Matteo at Prick (cnr of Old St/ Hackney Road/ Shoreditch HS.) He did a brilliant job and a very nice guy too.
It was all clean, tidy and he made a point of showing me that he was using new needles etc. (The owner Henry Hate is a bit of a celeb tattooist but is very grumpy - best to avoid him! lol)