Inverting the y-axis is a bit of a fudge, but this appears to fulfill your reqs:

#!/usr/bin/perl
use strict;
use warnings;

# running-times 15-05-05
#
# Graphing all my running times.
# I will just insert the data
# directly into this program for now,
# but when it becomes too much, Ill
# move it into another file/dbm

use GD::Graph::linespoints;
use Getopt::Std;

my %times;  # running times
my $chart;  # the GD::Graph::linespoints object
my $plot;   # the GD object containing the actual graph

my @DAYS = qw(Mon Tue Wed Thu Fri Sat Sun);

# process options

my %Opt;
getopts('ho:', \%Opt);
if ($Opt{h} or !$Opt{o}) {
  die "Usage:\n\t$0 -o outfile.png \n";
}

# Running times

%times = (
    "Mon" => "25.40",
    "Tue" => "24.20",
    "Wed" => "22.50",
    "Thu" => "23.30",
    "Fri" => "21.10",
    "Sat" => "24.30",
    "Sun" => "25.19",
);


# build graph
$chart = GD::Graph::linespoints->new( 480, 320, 1);
$chart->set(
    x_label => "Day",
    y_label => "Time (mins)",
    y_min_value => -26,
    y_max_value => -20,
    markers => [ 4 ],
    show_values => 1,
    y_number_format => sub{ return abs $_[ 0 ] },
    values_format => sub{ return abs $_[ 0 ] },
    title   => "Running Times for 5km - W/E May 15th 2005"
);
$plot = $chart->plot(
    [
        [ @DAYS ],
        [ map{ -$_ } @times{@DAYS} ],
    ]
);
# save it

open(F, "> $Opt{o}")
  or die "Can't open $Opt{o} for writing: $!\n";
print F $plot->png;
close F;

# Create html page with png in it

open H, ">times.html"
  or die "Can not create webpage: $!\n";

use CGI;

my $query = CGI->new( );

print H $query->start_html(-title=>'Gavins Weekly Running Times');
print H $query->p("Here are your times:");
print H "<table><tr><td><img src=$Opt{o}></a></td></tr></table>";
print H $query->end_html( );
close H;
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