There are no direct flights from Manchester,
http://www.manchesterairport.co.uk/MANInfo/All Destinations
so the journey time would depend upon where the connection was made (and the layover time at that point).
Korean Air quotes 10 hours 55 minutes from London (Heathrow) to Seoul. So add an hour or so for a flight from Manchester to Heathrow, plus time to change planes, and you might be looking at something in the region of 15 hours.
Other suitable connecting points might be Paris (CDG) or Frankfurt. The total journey time would probably be roughly the same, irrespective of the route chosen.
Of course, if you were seeking to get to a destination other than Seoul, you'd have to add on the time for the domestic connecting flight (plus the layover in Seoul).
Chris