Bordon isn't a *million miles from. Alton
and heading West, one might reasonably expect to head via Alton to join the A31.
*I would be very surprised if it is even 4 miles away. 
No idea where it is, would have to look at a map. But if I was near Basingstoke for example, I think I'd be more inclined to go to Newbury and M4/M5 it, rather than sit with the handbrake on on the A303.
Though if I was in Basingstoke, a fast trip out in any direction to get as far away as I can would be a great plan.
Shared route
From Bordon to Brixham via A303.
3 hr 43 min (164 mi)
3 hr 43 min in current traffic
Avoiding motorways
1. Head south on Essex Rd
2. Turn right to stay on Essex Rd
3. Turn left onto Lamerton Rd
4. Turn right onto Budds Ln
5. Turn left onto Oakhanger Rd
6. Turn left onto Hartley Mauditt
7. Turn left at Blanket St
8. Turn right onto Selborne Rd/B3006
9. At the roundabout, continue straight onto Selborne Rd/A339
10. At the roundabout, continue straight onto Whitedown Ln/A339
11. Turn left onto Spain Ln
12. Turn right onto Red Ln
13. Turn left to stay on Red Ln
14. Turn left onto Berrydown Ln
15. Turn right onto B3046
16. Turn left onto Dummer Rd
17. Turn left onto A30
18. Use the left lane to take the A303 slip road to A30/Andover
19. Continue onto A303
20. At Countess Roundabout, take the 2nd exit onto Amesbury Byp/A303
21. Exit the roundabout onto Amesbury Byp/A303
22. At Longbarrow Roundabout, take the 2nd exit and stay on A303
23. Exit the roundabout onto A303
24. At Hazelgrove Roundabout, take the 3rd exit and stay on A303
25. Exit the roundabout onto A303
26. At Podimore Roundabout, take the 2nd exit and stay on A303
27. Exit the roundabout onto A303
28. At Cartgate Roundabout, take the 2nd exit and stay on A303
29. Exit the roundabout onto A303
30. At Hayes End Roundabout, take the 3rd exit onto Ilminster Byp/A303
31. Exit the roundabout onto Ilminster Byp/A303
32. At Southfields Roundabout, take the 2nd exit onto A303
33. Exit the roundabout onto A303
34. At Moor Lane Roundabout, take the 2nd exit and stay on Honiton Rd/A3015
35. Exit the roundabout onto Honiton Rd/A3015
36. At the roundabout, take the 1st exit onto A3015
37. Slight left onto Hill Barton Rd/A3015
38. At Middlemoor Roundabout, take the 2nd exit onto Rydon Ln/A3015
39. Exit the roundabout onto Rydon Ln/A3015
40. Turn left onto Russell Way
41. At the roundabout, continue straight to stay on Russell Way
42. At the roundabout, continue straight to stay on Russell Way
43. Keep right to stay on Russell Way
44. Use the left lane to turn right onto A379
45. Keep left at the fork, follow signs for City Centre/Dawlish/A379/Marsh Barton/Topsham
46. At Countess Wear Roundabout, take the 2nd exit onto Bridge Rd/A379
47. Exit the roundabout onto Bridge Rd/A379
48. Slight right to stay on Bridge Rd/A379
49. At the roundabout, take the 2nd exit and stay on Bridge Rd/A379
50. Exit the roundabout onto Bridge Rd/A379
51. At the roundabout, take the 2nd exit and stay on A379
52. Exit the roundabout onto A379
53. Take the A38 slip road on the right to Plymouth/Torquay/A380
54. Use the left 2 lanes to turn slightly left onto A380 (signs for Torquay)
55. Keep right to continue on Besigheim Way/Penn Inn Flyover/A380
56. At the roundabout, continue straight onto Hellevoetsluis Way/A380
57. At the roundabout, take the 2nd exit onto Marldon Way/A380
58. Exit the roundabout onto Marldon Way/A380
59. At the roundabout, take the 2nd exit onto Kings Ash Rd/A380
60. Exit the roundabout onto Kings Ash Rd/A380
61. Turn left onto Waterleat Rd
62. Turn right onto Dartmouth Rd/A379
63. Turn left onto Market St
64. Turn right towards Brewery Ln
65. Turn left onto Brewery Ln
66. Keep right
67. Turn right
68. Arrive at location: Brixham
For the best route in current traffic visit
https://maps.app.goo.gl/o5vWzZ4BvRrbhN1aA