Your neighbours extension is a detached house and doesn’t appear to be on the boundary hence they can go higher with the parapet wall.
Presently you need to submit for permitted development or notification of a larger home extension and will have to have I complete by May 2019 iirc. After this the may revert back to a maximum of 3.0m for a semi detached rear extension.
I expect that the rule will remain in place after that date though as it’s already been extended.
I really don’t get why it wasn’t just incorporated into a planning application process. We have secured the permitted development process and are presently awaiting a verdict from planning for the side extension to go with it. A slow process but hopefully everything will be in order in a couple of weeks time…
Good luck, lose the parapet and your good to submit I reckon.