This graph was produced in Excel. The GIF from excel, with transparent background, was converted with GIMP to non-transparent PNG, as that works better for WP.
Date, LabourMembers, Other data source
1928-12-31, 215000
1929-12-31, 228000
1930-12-31, 277000
1931-12-31, 297000
1932-12-31, 372000
1933-12-31, 366000
1934-12-31, 381000
1935-12-31, 419000
1936-12-31, 431000
1937-12-31, 447000
1938-12-31, 429000
1939-12-31, 409000
1940-12-31, 304000
1941-12-31, 227000
1942-12-31, 219000
1943-12-31, 236000
1944-12-31, 266000
1945-12-31, 487000
1946-12-31, 645000
1947-12-31, 608000
1948-12-31, 629000
1949-12-31, 730000
1950-12-31, 908000
1951-12-31, 876000
1952-12-31, 1015000
1953-12-31, 1005000
1954-12-31, 934000
1955-12-31, 843000
1956-12-31, 845000
1957-12-31, 913000
1958-12-31, 889000
1959-12-31, 845000
1960-12-31, 790000
1961-12-31, 751000
1962-12-31, 767000
1963-12-31, 830000
1964-12-31, 830000
1965-12-31, 817000
1966-12-31, 776000
1967-12-31, 734000
1968-12-31, 701000
1969-12-31, 681000
1970-12-31, 680000
1971-12-31, 700000
1972-12-31, 703000
1973-12-31, 665000
1974-12-31, 692000
1975-12-31, 675000
1976-12-31, 659000
1977-12-31, 660000
1978-12-31, 676000
1979-12-31, 666000
1980-12-31, 348000
1981-12-31, 277000
1982-12-31, 274000
1983-12-31, 295000
1984-12-31, 323000
1985-12-31, 313000
1986-12-31, 297000
1987-12-31, 289000
1988-12-31, 266000
1989-12-31, 294000
1990-12-31, 311000
1991-12-31, 261000
1992-12-31, 280000
1993-12-31, 266000
1994-12-31, 305000
1995-12-31, 365000
1996-12-31, 400000
1997-12-31, 405000
1998-12-31, 388000
1999-12-31, 361000
2000-12-31, 311000
2001-12-31, 272000
2002-12-31, 248000
2003-12-31, 215000
2004-12-31, 201000
2005-12-31, 198000
2006-12-31, 182000
2007-12-31, 177000
2008-12-31, 166000
2009-12-31, 156000
2010-12-31, 193000
2011-12-31, 193000
2012-12-31, 187000
2013-12-31, 189531, 2014 accounts: http://search.electoralcommission.org.uk/Api/Accounts/Documents/16479
2014-12-31, 193754, 2014 accounts: http://search.electoralcommission.org.uk/Api/Accounts/Documents/16479
2015-05-06, 201293, https://www.theguardian.com/politics/2016/jan/13/revealed-how-jeremy-corbyn-has-reshaped-the-labour-party
2015-08-25, 292505, http://www.mirror.co.uk/news/uk-news/four-labour-leadership-candidates-rule-6316659
2015-12-31, 388262, 2015 accounts: http://search.electoralcommission.org.uk/Api/Accounts/Documents/17488
2016-01-10, 388407, http://www.theguardian.com/politics/2016/jan/13/revealed-how-jeremy-corbyn-has-reshaped-the-labour-party
2016-06-30, 450000, http://www.independent.co.uk/news/uk/politics/labour-party-gains-60000-new-members-following-attempted-coup-against-corbyn-a7112336.html