A better solution might be  ((?:<[^>]*>)+)

(?:<[^>]*>)+ or even just plain  (?:<[^>]*>) allows a pair of tags with no intervening blanks to match or to be excluded from matching, respectively, thereby potentially destroying open-tag/close-tag synchronization: in either case, the "pair" of tags between which blanks are eliminated is incorrect. This can be remedied by changing the quantifier on  $blank, but, as another reply has suggested, a proper HTML parser is really the best approach.

>perl -wMstrict -le
"my $s = '<foo a=b></foo>   <bar c=d>   </bar>   ';
 my $t;
 ($t = $s) =~ s@((?:<[^>]*>)+) +((?:<[^>]*>)+)@$1$2@g;
 print qq{'$t'};
 my $tag   = qr{ < [^>]* > }xms;
 my $blank = qr{ [ ] }xms;
 ($t = $s) =~ s{ ($tag) $blank+ ($tag) }{$1$2}xmsg;
 print qq{'$t'};
 ($t = $s) =~ s{ ($tag) $blank* ($tag) }{$1$2}xmsg;
 print qq{'$t'};
 print qq{'$s'};
"
'<foo a=b></foo><bar c=d>   </bar>   '
'<foo a=b></foo><bar c=d>   </bar>   '
'<foo a=b></foo>   <bar c=d></bar>   '
'<foo a=b></foo>   <bar c=d>   </bar>   '
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Update: Added another example using  * quantifier.