Oh, hadn't realised it's in Cumbria on the trig database..... looking at the map it can only be a few metres out of Northumberland.
I've had a quick measuring session with a ruler on the 1:25000 maps and as far as I can see Glendhu Hill is the remotest of the Kielder area trigs: it's 6.5km in a straight line from the end of the road at Dykecrofts (in Scotland). Berrymoor Edge runs it a close second if you don't count the Kielder Forest Drive (which closes over winter) as a public road. Taking a straight line from Berrymoor Edge you'd need to swim across the Catcleugh reservoir to reach the nearest road in less than 6.5km. In my own home area (North Pennines), although there are trigs that need a long boggy walk to reach, none of them can beat Glendhu Hill because of the number of very high roads crossing the moors between dales.
What about The Lakes or Dartmoor, which I would guess are the other two possible areas for remote trigs?
A clever person with the trig database, OS vector maps data, and a GIS programme could give a definite answer, but it wouldn't be easy!