To make sure everything is formatted correctly I'd be interested to see the value of the $url variable just before it's passed to fopen(). Also, you might want to add an error message, ie:
$url = "http://www.domain.co.uk/mail/signup.php?list=1&email=$payer_email&fname=$first_name&seq=1&del=0&overwritedupes=1";
echo "LMPURL=$url<br>";
$lmp = fopen($url,'r');
if(!$lmp) echo "LMPERROR=Didn't open URL?<br>";
fclose($lmp);