No mail error but no mail sent!

[rrabbit]

I'm trying to do a simple form mail using mail():
[pre]<?php
$email = $_POST["email"];
$subject = $_POST["subject"];
$message = $_POST["message"];
$to = 'mid.chiswick@tesco.net';
$headers = "From: $email";
if (mail($to, $subject, $message, $headers)) {
echo "Your mail has been sent to $to.";
} else {
echo "Your mail could not be sent.";
}
?>[/pre]

The script works OK and returns the message that says the mail has been sent. But it never arrives. I guess something is not set up correctly on the server, but being a bit of a newbie I'm not sure what questions to ask my ISP. Or am I doing something else wrong? Any help much appreciated.