Taking driving distances, a few of the answers so far have missed that the locations may be closer to stations on a different line. For example Essendine is a long way from anything on the ECML, but under 5 miles from Stamford station. Tebay's nearest station is also on a different line (Kirkby Stephen), though it is still quote far at 10 miles. Another I thought of was Grantshouse on the ECML in the Scottish Borders, which is 12 miles from Dunbar.
However in terms of absolute distance, the Scottish examples on the WCML are the furthest given so far - Abington is 20 miles from its nearest station in Carstairs. Although in terms of size, Coalville at just over 10 miles to Loughborough or Rothely and Garstang at just under 11 miles to Lancaster (further on the way back due to the city's one-way system!) might be more notable.
Abington, Crawford?
There are a whole string of sizeable such places in the area. Somerton and Langport to the east of Taunton, and Wellington and Cullompton to the west, are all significant sized settlements (Wellington is certainly a town, and Somerton and Cullompton are close to being so) with a passenger railway running right through the middle of them but no station. If the line had been run by the same management as do the old Southern Exeter to Salisbury line I'm sure they would have stations, either retained or reopened.Somerton in Somerset is on a fairly long stationless stretch, although it won't be the greatest being about 12 miles from Castle Cary by road.
The issue is whether there is any suitable passenger service on the line. Coalville and Ashby are on a freight-only line, which I believe is no longer continuous from Leicester to Burton. And other proposals need to take account of the type of service. The Somerton and Langport examples I give would be impractical with the current service, which is only Inter-City trains running down to Devon and Cornwall, although there is certainly scope for an intermediate stations service from Paddington to Taunton or Exeter, allowing the through service to be speeded up. Village station proposals on main lines often fall foul of this. Stopping an existing stopping service is far more straightforward than starting a new service which has to generate a trainload from scratch. Regarding say Somerton, consideration of where the travel demand is to is also key - the nearest significant town is Yeovil, and the nearest major urban area is Bristol, both of which will have developed links to the town but are not served by any rail service to the new station.Maybe these places and Coalville and Ashby actually should have stations given how big they are
And indeed national rail services...I think Okehampton (about 20 miles from Exeter and on the freight line to Meldon Quarry) would be in the running, but it does have a seasonal heritage railway service so probably doesn't count.
The issue is whether there is any suitable passenger service on the line. Coalville and Ashby are on a freight-only line, which I believe is no longer continuous from Leicester to Burton. And other proposals need to take account of the type of service. The Somerton and Langport examples I give would be impractical with the current service, which is only Inter-City trains running down to Devon and Cornwall, although there is certainly scope for an intermediate stations service from Paddington to Taunton or Exeter, allowing the through service to be speeded up. Village station proposals on main lines often fall foul of this. Stopping an existing stopping service is far more straightforward than starting a new service which has to generate a trainload from scratch. Regarding say Somerton, consideration of where the travel demand is to is also key - the nearest significant town is Yeovil, and the nearest major urban area is Bristol, both of which will have developed links to the town but are not served by any rail service to the new station.