The fastest route can be done fairly easily just by road signs. It's not a pleasant route, but it sure is fast! No need for unlimited time, nor the compass.
A30 to Exeter
Exeter follow Honiton (A30) onto the A377, City Centre, inner Bypass, B3212-Pinhoe-B3181
A38 to Worcester, A449 to Kidderminster, A442 to Bridgnorth, A458 to Shrewsbury
A49 to Preston via Warrington (touches A5). A6 to Carlisle, A7 in Carlisle, left onto former A74 jsut before M6 junction.
B7076 to Abington, A702 twd Biggar, A73, Thankerton, Carnwath, A70 twd Edinburgh. B7031 Kirknewton, A71 twd Edinburgh
B7030, A8, left immediately, right B800, right A9000, right B981 I'keithing, left B917, left B996, onto A922.
Right rbt Milnathort A911, left Perth B996, A912 Perth
A9 - A99 - JOG
Most of the cues are following old roads that have been replaced by motorways. If you were able to use motorways:
A30-M5-M6-A74(M)-M74-M73-M80-M9-A9-A99
Is the quickest car route, and the same sort of distance (837 mi).