First let me agree with the above advice that usnig a specialist HTML parser is the best option. This said here is the solution you want: 

$_ = '<a href="foo">/path/sub/dir</a>';
$d = '/path';
$d = quotemeta $d;
print $1 if /"\s*>.*?$d(.*?)<\/A>/i;

# prints /sub/dir

# here it is with the regex expanded

$_ = '<a href="foo">/path/sub/dir</a>';
$d = '/path';
$d = quotemeta $d;
print $1 if m       # match regex
            /       # opening delim
            "       # literal "
            \s*     # plus 0 or more spaces
            >       # end of <a href tag
            .*?     # some leading stuff (minimum)
            $d      # our path
            (.*?)   # out subdirs captured into $1
            <\/A>   # the closing tag
            /ix;    # /i => case insensitive for </a> tag
                    # /x => allow comments

[download]

You need the quotemeta to make $d safe to interpolate into the regex, otherwise the / used as a path delimiter will be misinterpreted as the closing regex delimiter ie after interpolating $d the regex would be /"\s*>.*?/path(.*?)<\/A>/i

cheers

tachyon

s&&rsenoyhcatreve&&&s&n.+t&"$'$`$\"$\&"&ee&&y&srve&&d&&print

In reply to Re: regexp problem by tachyon
in thread regexp problem by Ignatius Monk

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