I have no idea why you're trying to do this, but the following code should work as specified:

use strict;
use warnings;

my $str = '&nbsp; <x &nbsp;<y &nbsp;>>';
my $c = 0; my @arr;
while ($str =~ /<[^<>]+>/) {
    $str =~ s/<([^<>]+)>/`$c`/;
    $arr[$c++] = $1;
}
s/&nbsp;/"/ig for @arr;
while ($str =~ /`\d+`/) {
    $str =~ s/`(\d+)`/<$arr[$1]>/g;
}
print $str;
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The hard part is dealing with nested tags, but if you start with the inside tags and work outwards, you have no real problems.