I have compiled a list of UK LLM groups on lawyrs.net including signup links for those who haven't joined the lawyrs network yet. I have also listed some non-LLM groups, which I thought could be useful for other LLM-Guide users. If you find other interesting groups, please post them below!
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LLM Groups:

LLM-Guide Group (66 members)
www.lawyrs.net/groups/6/llm-guide
Signup link: www.lawyrs.net/llmguide/6

Cambridge LLM 2009 (29 members)
www.lawyrs.net/groups/68/cambridge-llm-class-of-20…
Signup link: www.lawyrs.net/llmguide/68

Oxford Class of 2009 (18 members)
www.lawyrs.net/groups/28/oxford-class-of-2009
Signup link: www.lawyrs.net/llmguide/28

UCL LLM 2009 (55 members)
www.lawyrs.net/groups/34/ucl-llm-class-of-2009
Signup link: www.lawyrs.net/llmguide/34

LSE LLM 2009 (23 members)
www.lawyrs.net/groups/32/lse-llm-class-of-2009
Signup link: www.lawyrs.net/llmguide/32

Queen Mary LLM 2009 (23 members)
www.lawyrs.net/groups/57/queen-mary-llm-20082009
Signup link: www.lawyrs.net/llmguide/57

King’s College LLM 2009 (27 members)
www.lawyrs.net/groups/43/kings-college-london-llm-…
Signup link: www.lawyrs.net/llmguide/43

Edinburgh LLM 2009 (3 members)
www.lawyrs.net/groups/58/edinburgh-llm-20082009
Signup link: www.lawyrs.net/llmguide/58

Other groups:

Law Firm Networking
www.lawyrs.net/groups/66/law-firm-networking
Signup link: www.lawyrs.net/llmguide/66

In-House Lawyers
www.lawyrs.net/groups/54/in-house
Signup link: www.lawyrs.net/llmguide/54

Tax Consultants
www.lawyrs.net/groups/19/tax-consultants
Signup link: www.lawyrs.net/llmguide/19

Criminal Lawyers
www.lawyrs.net/groups/15/criminal-lawyers
Signup link: www.lawyrs.net/llmguide/15

Intellectual Property Law Group
www.lawyrs.net/groups/21/intellectual-property
Signup link: www.lawyrs.net/llmguide/21

Human Rights
www.lawyrs.net/groups/14/human-rights
Signup link: www.lawyrs.net/llmguide/14

WTO Law
www.lawyrs.net/groups/49/wto-law
Signup link: www.lawyrs.net/llmguide/49

WTO and Environment
www.lawyrs.net/groups/50/wto-and-environment
Signup link: www.lawyrs.net/llmguide/50

Lawyers’community in China
www.lawyrs.net/groups/51/lawyers-community-in-chin……
Signup link: www.lawyrs.net/llmguide/51

American Lawyers
www.lawyrs.net/groups/17/american-lawyers
Signup link: www.lawyrs.net/llmguide/17

French Lawyers
www.lawyrs.net/groups/22/french-lawyers
Signup link: www.lawyrs.net/llmguide/22

Italian Lawyers
www.lawyrs.net/groups/8/italian-lawyers
Signup link: www.lawyrs.net/llmguide/8

English Lawyers
www.lawyrs.net/groups/16/english-lawyers
Signup link: www.lawyrs.net/llmguide/16

Pakistani Lawyers
www.lawyrs.net/groups/45/pakistani-lawyers
Signup link: www.lawyrs.net/llmguide/45

Africa Business Law
www.lawyrs.net/groups/18/africa-business-law
Signup link: www.lawyrs.net/llmguide/18

Brazil
www.lawyrs.net/groups/65/brazil
Signup link: www.lawyrs.net/llmguide/65

Abogados Mexicanos
www.lawyrs.net/groups/46/abogados-mexicanos
Signup link: www.lawyrs.net/llmguide/46

Oxford Alumni
www.lawyrs.net/groups/23/oxford-alumni
Signup link: www.lawyrs.net/llmguide/23

Delhi University
www.lawyrs.net/groups/72/
Signup link: www.lawyrs.net/llmguide/72

I can’t believe it’s a law firm – Fans of Lionel Hutz
www.lawyrs.net/groups/48/i-cant-believe-its-a-law-……
Signup link: www.lawyrs.net/llmguide/48

Hello, there is a group for Indian lawyers as well: http://www.lawyrs.net/llmguide/76