I prefer to write my regexes as restrictive as possible. Hence, something like (untested):

$file =~ m{<TABLE \s+ ([^>]*+)>
           (
              [^<]*+ (?: < (?!/TABLE>) [^<]*+ )*
           )
           </TABLE>}x;
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This puts 'name="table1"' in $1 and the content of the table in $2. If the perl you're using is pre-5.10, or if you know your input is 'valid' (that is, each <TABLE> has a matching </TABLE>) use '*' instead of '*+'.