Here's a vulgar-minded approach (no advanced algorithmics or smart intermediary data structures). Also I'm not sure if I understand correctly your idea of "linking" (though the code works for your examples):

for (keys  %$start) {
  my @all = ($_, keys %{$start->{$_}});

  my $processed;

  for my $setref (@$end) {
    my (@found, @not_found);

    for my $item (@all) {
      push @found, grep {$item eq $_} @$setref;
    }

    if (@found) {
      for my $item (@all) {
        push @not_found, $item unless grep {$item eq $_} @found;
      }

      push @$setref, @not_found
        if @not_found;
      $processed++;
    }
  }
  push @$end, [ @all ]
    unless $processed;
}
[download]

Update: Please take into account that the code takes a few shortcuts. It makes no assumptions about the value in inner hashes (in your examples they're all "1"), and it doesn't handle well items linking to themselves (a => {a => 1, b => 1}) in some cases. These issues are easy to fix, though.

Update 2: Nope, it won't work, consider data below, and I don't think there's a solution that doesn't employ "advanced algorithmics" ;)

my $start =
  {
   a => {b => 1},
   c => {d => 2},
   d => {a => 1}
  };
[download]