This works for me:

use strict;
use Regexp::Common qw /URI/;

my $big_string;

while (<DATA>) {
    chomp;
    $big_string .= $_;
}
my @websites = $big_string =~ m/($RE{URI}{HTTP})/g;

print join "\n", @websites;

__DATA__
This is a test this is a test test test http://www.website.
com/getme.html this is test this is a test
This is a test this is a test test test http://www.website2.com/
getme.html this is test this is a test
This is a test this is a test test test http://www.website3.com/getme
.html this is test this is a test
This is a test this is a test test test http://www.website4.com/getme.
+h
tml this is test this is a test
[download]

Its output is:

http://www.website.com/getme.html
http://www.website2.com/getme.html
http://www.website3.com/getme.html
http://www.website4.com/getme.html
[download]