Since you specifically asked about a solution using sed... Assuming that the interesting lines are always between lines containing <pre>
and </pre>
(appearing exactly like that) and that the interesting content is never on the same line than the opening or closing tag, and assuming that the first such block is the only one you want to extract, and assuming that while you understand that this is really the wrong way to solve this problem you still want to do it, then you could do this using sed for example like this:
sed '1,/<pre>/d;/<\/pre>/,$d'
It deletes all lines from the first up to the one containing <pre>
and all lines from the one containing </pre>
to the last.
(FWIW, I would rather use an XPath expression for selecting the interesting content. For example using xmlstarlet as suggested by Ignacio Vazquez-Abrams it could go like this: xmlstarlet sel -t -v /html/body/pre
.)