https://www.hyndburnbc.gov.uk/the-mayors-office/7/ list them and their dates of office.
So you have a choice of:
1919 – 1920 : David Walton Muffit
1920 – 1922: James Waddington
1922 – 1923 : Edward Woolley
1922 – July 1925: Frederick Lord. Died in Office, July 1925
July 1925 – 1927 : Charles Wilkinson
1927 – 1928 : T E Higham
1928 – Feb 1930 : Richard Watson. Died in office, Feb 1930