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Well, bitd (as you put it) the club finishing bottom of the English football league would apply for re-admission. ....
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All the 4 sides at the bottom of the Football League had to apply for re-election, not just the bottom side.
Before the formation of the Conference/ National League in 1979, any club could apply for promotion and often there were multiple non league clubs applying, thus splitting the votes for the non league sides.
The Conference was formed with the aim of only the winners of the conference applying for promotion. I believe it was a condition of membership of conference. Obviously this would not have stopped sides in say Isthmian or Northern Leagues applying if they wanted to as they were not part of pyramid in those days, but they were mainly the traditionally amateur clubs anyway
For the first 7 seasons of the Conference, there was no automatic promotion and none of the winners got promoted
Season National League Champions
1979–80 Altrincham
1980–81 Altrincham
1981–82 Runcorn
1982–83 Enfield
1983–84 Maidstone United
1984–85 Wealdstone
1985–86 Enfield
The formation of the Conference came towards the end of Altrincham's dominance of non league football. They won the first 2 and never again.
1In 1987 Scarborough ( RIP) were the first club to gain automatic promotion under a then unknown manager (Colin ......)
Altrincham never won Conference again, although they did win the FA Trophy in 1986 v Runcorn