Since the post is very old, but i want to tell so it will help people who need to travel from LHR - MZF directly. Yes there is a direct bus service from Lahore to Muzaffarabad.
Sirinagar Express
General Bus Stand Badamibagh
Timings 10:00PM - 11:30PM (Not sure as i travelled years back)
You have to confirm at your own about timings and fares. But Yes, there is a direct bus service from LHR - MZF