Leaving aside the conferences and concentrating on the Premier League, the Football League Championship, Football League One and Football League two in England you'll get 23 clubs:
Arsenal, Barnet, Barnsley, Blackpool, Brentford, Burnley, Bury, chelsea, Chesterfield Everton, Fulham, Gillingham, Liverpool, Millwall, Morecambe, Portsmouth, Reading, Rochdale, Stevenage, Sunderland, Walsall, Watford and Wimbledon.
In total the Scottish Premier League and the First, Second and Third Division come up with thirteen clubs:
Arbroath, Celtic, Clyde, Dumbarton, Dundee, Falkirk, Livingston, Montrose, Motherwell, Peterhead, Rangers, Stenhousemuir and Stranraer
So all in all there are 35 clubs with just one name, but only if you consider the four highest leagues in both countries.
Sep 18 2012, 3:57 PM