Here is the distribution map and below that the full list.
Mark Vivis (b.1975) Amersham 2016
Andrew Muir North Down 2013-4
Guy Woodham (b.1968) Milford Haven 2012-2
William Elliott (b.1988) Milford Haven 2016-7
E. F. Benson (1867-1940) Rye 1934-7
Sir Roland Gwynne (1882-1971) Eastbourne 1928-31
Sir Charles Irving (1924-1996) Cheltenham 1958-60, 1971-2
Brian Coleman (b.1961) Barnet 2009-10
Marc Cranfield-Adams (b.1960) Richmond-upon-Thames 2007-8
Bob Crossman (1946-1996) Islington 1986-7
John Gallagher (b.1948) Ealing 2011-2
Philip Glanville Hackney 2016-7
Jeff Hook (b.1954) Southwark 2009-10
Jonathan Simpson (b.1970) Camden 2010-11, 2013-4
Wayne Trakas-Lawlor (b.1966) Croydon 2016
Christopher Wellbelove Lambeth 2009
John Sam Jones (b.1960) Barmouth 2014-15
Hereford and Worcester
William, 7th Earl Beauchamp (1872-1838) Worcester 1895-6
Allan Amos (b.1952) Worcester 2014-5
Francis Bennett-Goldney (1865-1918) Canterbury 1906-11
Lancashire (now part of Greater Manchester)
Sir Cyril Smith (1928-2010) Rochdale 1966
Ian Campbell (b.1987) Retford 2010-11
Mike Wolfe (b.1951) Stoke on Trent 2002-5
Mark Meredith (b.1965) Stoke on Trent 2005-9
Sahran Abeysundara (b.1974) Haslemere 2016-17
Andrew Street (b.1963) West Midlands 2017
In addition to these mayors there have been three Deputy Mayors of London, Sir Simon Milton and Richard Barnes (both in office 2008-11) and Roger Evans (2015-16).
One particularly interesting statistic from an lgbt point of view is that between 2002 and 2007 Stoke-on-Trent had two directly elected mayors and both of them were gay men. Prior to that, and since 2009, the mayor has been selected in the traditional manner by being appointed by the elected councillors. The idea of having a directly elected mayor, as is common in the USA, was a trend begun in the 1990s. Not all cities or municipalities were considered appropriate for such a system but the decision was left to a public referendum in each place. A referendum was held here in Nottingham and we rejected the idea. In Stoke-on-Trent the electorate later voted to abolish the directly elected mayor and return to the traditional appointed mayor.
One area which voted for a directly elected mayor was the county of West Midlands. Generally county councils comprise elected representatives from the towns, city councils and boroughs within them. The leaders of county councils are not generally directly elected by the public. This system explains why there is both a Lord Mayor of London and a Mayor of London. The Lord Mayor is the head of a borough and the Mayor is the head of the county of Greater London.
In 2010 Ian Campbell made national headlines in the UK when he became the youngest mayor in the country at the age of 23 when he was appointed Mayor of Retford, a town I know very well as it is the nearest large town in rural north Nottinghamshire to where I was raised. It is also a place, like my present home in Nottingham, where I have an ancestral connection. As well as being descended from John Tansley, Mayor of Nottingham twice (1399 and 1410), I am also descended from Robert Smeaton who was Senior Bailiff of Retford in 1632 (Senior Bailiff was an alterative title for Mayor; Retford last used the title Senior Bailiff and have used the title Mayor since the 1850s).
A final lgbt mayor to mention is an honorary one. During the London 2012 Olympic Games the athletes’ village had an honorary mayor for the duration of the Olympic and Paralympic Games. He was Charles Allen, the Director of the London Organising Committee (LOCOG) who had also been Vice-Chair of the London 2012 Bid. In 2012 he was appointed a life peer with the title Lord Allen of Kensington.
As with all published material the data given in all these Chain Male articles may well be out of date before too long as more elections place lgbt members into mayoral office.