Hello all,
I run a website called "Swing Junction" -
Swing Junction-Lindy Hop Events, Classes, Forum & info in UK - which lists most of the Lindy Hop & Balboa classes in the UK. The main calendar can be filtered to display just the London region stuff.
I've since moved back to Edinburgh but whilst living in London, I went to London Swing Dance Society @ 100 Club, Swingland's C-Jam, Jump'n'Jive (they teach Lindy Hop, not Jive on Monday nights in Ealing) and Dan Guest's Lindy Circle on Friday night.
I never made it to Julie's Jitterbug nights but no reason you shouldn't check it out
There are many more nights, but these were nights I mainly went to. Swing Junction also has links back to the Lindy Hop schools and venues.
...A quick run down...
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C-Jam is known as the night when most of the best dancers get out and it's DJ'ed music. Martin Ellis runs the night. I don't know much about Martin but he also runs a major yearly events in London that attracts dancers from all over Europe, I believe.
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100 Club has a live band with Simon Dj'ing between sets. Simon travels internationally to teach Lindy Hop. Some of my burlesque attending friends go here too! The bands normally play a mix of Jive music and Lindy Hop music (Lindy Hop music is more jazz based than Jive music). Simon tends to DJ more Lindy Hop music.
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Jump'n'Jive - Andy and Rena teach Monday nights in Ealing. There isn't much dancing after or between classes but the people are great and lots of emphasis on playing with the music and your partner. These guys are also my most favourite aerials (air-steps) teachers in the world - I prefer them to the Swedes even

. They are also lovely people and teach interesting and old-school Lindy Hop moves. These guys travel to teach and also run dance camps that attract international dancers.
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Lindy Circle is now run by Dan guest and is known internationally for Lindy Hop but primarily for Balboa (a style of dance to the same music as Lindy Hop but intended for crowded room and only fast music). There is plenty of dancing after classes and you can learn Balboa and Lindy Hop on the same night. There is lots of footage of Dan, and his ex-partner Christie, on YouTube. He's also a nice guy

. I didn't have many classes with him but do regret not making more of an effort.
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I've been told to recommend seeking out Ryan Francois and Jenny Thomas (aka Ryan & Jenny). Ryan has choreographed for Hollywood films and together they have had US T.V appearances and run Camp Savoy - also a well known dance camp. They travel extensively in and out of the UK so I don't believe if they teach regular classes at the moment but they were planning on it. They are based in Guilford methinks. Unfortunately, I've never had the opportunity to meet them or learn from them.
I hope this information helps and you find my website of value
Regards,
Ben