From
Beautiful Britain9th October 1897 Henry Stumey set off in his 4.5hp Daimler from Land's End, and became the first person to drive to John o' Groats. His 929 mile journey took him 10 days.
Google tells me ...by car
14 hr 34 min (837.2 mi) via A9
I question the safety of driving without a significant break
and Google by public transport
06:49 (walk to Sennen Cove) - 12:21 next day
07:20 from Sennen Cove - "Land's End Coaster" bus to Penzannce 08:38
Train - change Plymouth, New Street, Preston, Haymarket
Overnight in Inverness - 23:19 to 07:00
Train to Thurso (10:59)
Bus at 11:30 for that 12:21 arrival
GWR▸ is only offering me two services a day - both by sleeper at over £300