It is never the intention that the route will be the shortest path between  two points. The dominating concern is to keep as close to the line as possible whilst keeping the walk safe, legal and practical. Avoidance of roads is also a consideration in particular in relation to heavy traffic and your safety. Because of the choice of PROWs {Public Rights Of Way] in preference to other routes you will often be using seldom frequented paths meaning they might be overgrown with vegetation or, commonly, landowners resent you using little known paths across their  property to which you have absolute legal right of access. For the former problem I suggest you carry a light pair of secateurs and the latter, read and know the detail of the  duties of landowners with regard to PROWs from the UK Government website reproduced below : https://www.gov.uk/guidance/public-rights-of-way-landowner-responsibilities  . For most purposes an Ordnance Survey 1:25000 map will show  rights of way as dashed green lines with variations to indicate footpaths, bridleways or national trails that cross private land (see the key for the map).   If you do come across an assertive landowner it is useful to know that it is an offence for them to threaten you in any way and the same rule applies to you of course. Therefore be calm and firm and show the PROW on the map to them. It is possible that you have misread the map.