Here is a (fairly complete) Wikipedia list of UK think tanks: https://en.wikipedia.org/wiki/List_of_think_tanks_in_the_United_Kingdom
Non-aligned Think Tanks
- Local Government Information Unit: http://www.lgiu.org.uk/ Twitter: @LGiU
- The Institute for Fiscal Studies: http://www.ifs.org.uk/, Twitter: @TheIFS
- The Institute for Government: http://www.instituteforgovernment.org.uk/ Twitter: @instituteforgov
- The Institute for Public Policy Research: http://www.ippr.org/, Twitter: @IPPR Facebook: https://www.facebook.com/pages/ippr/120961521233
- The work Foundation: http://www.theworkfoundation.com/, Twitter: @WorkFoundation
Left of Centre Think Tanks
- Centre for Labour and Social Studies: http://classonline.org.uk/ Twitter: @Classthinktank Facebook: https://www.facebook.com/pages/Class-Centre-for-Labour-and-Social-Studies/278894568854115
- Labour Research Department: http://www.lrd.org.uk Twitter: @LRDunionnews Facebook: https://www.facebook.com/groups/66619604668/
- The Fabian Society: http://www.fabians.org.uk/, Twitter: @thefabians Facebook: https://www.facebook.com/fabiansociety
- Unions 21: http://www.unions21.org.uk Twitter: @Unions21 Facebook: https://www.facebook.com/groups/9980241281/
Right Wing Think Tanks
- Adam Smith Institute: http://www.adamsmith.org/, Twitter: @ASI
- Centre for Policy Studies: http://www.cps.org.uk/, Twitter: @CPSthinktank
- Policy Exchange: http://www.policyexchange.org.uk/, Twitter: @Policy_Exchange See also: https://en.wikipedia.org/wiki/Policy_Exchange#Newsnight_investigation
- Social Market Foundation: http://www.smf.co.uk/, Twitter: @SMFthinktank