I think its possible to ride out of the back of thre centre park, onto the Cliburn-A6 road,head west to Clifton-eamont bridge a6(avoid the dangerous a66 at all costs)from there take the road,(south) through the middle of Lowther caravan site (Eamont Bridge),theres some great singletrack along the river here on the left.
From Lowther Castle turn right onto the road downhill over a cattle grid keeping left before the bridge,join a track here that heads towards whale village,once onto the road turn right towards the Askham village Helton road.
Theres numerous Bridleways from Helton,or Askham and are pretty good singlespeed routes imho,nice gradual climbs.Its dry up there at the moment so the decent from moordivock to Howtown will be great. 😉
return via the road to Pooley bridge,Tirril,Eamont Bridge. enjoy.