<?php
$html = <<<EOT
<p><b>There are currently five entries in the London Borough of Barking & Dagenham (LBBD):</b></p>
<p>My string 1<br>
My another string<br>
And this is also my string<br></p>
<p><i>Some text over here</i></p>
EOT;
preg_match_all("/(<p>)?(.+)<br>/", $html, $matches);
print_r($matches);
Array
(
[0] => Array
(
[0] => <p>My string 1<br>
[1] => My another string<br>
[2] => And this is also my string<br>
)
[1] => Array
(
[0] => <p>
[1] =>
[2] =>
)
[2] => Array
(
[0] => My string 1
[1] => My another string
[2] => And this is also my string
)
)