<form action="anotherPage.php" id="database_submit" name="Form1">
<input type="text" name="Door Number" form="database_submit">
<input type="submit" value="Submit">
</form>


//when the below form is submitted it returns to this page
//and loses all data entered in the above form

<form action="page1.php" id="get_postcode" name="Form2">
<input type="text" name="getPostCode" form="get_postcode">
<input type="submit" value="Submit">
</form>

<input type="text" name="Door Number" form="database_submit"
style="display:none">
<input type="submit" value="Submit" style="display:none">

<form action="page1.php" id="get_postcode" name="Form2" method="post">

<?php
$dn = !empty($_POST['Door Number']) ? $_POST['firstname'] : '';

 ?>
<input type="text" name="Door Number" form="database_submit" value="<?php
 echo $dn;?>">