It appears to be having you on the A3 after Petersfield, that should be avoided to say the least, high speed dual carridge way with no safe cycling space.
The route to Petersfield looks good in my 'unknowledged of the area' eyes, Once you get to Petersfield, I'd recommend heading west to East Meon, then down to clanfield then back on that purple line from Clanfield and you're set.
It appears to be having you on the A3 after Petersfield, that should be avoided to say the least, high speed dual carridge way with no safe cycling space.
The route to Petersfield looks good in my 'unknowledged of the area' eyes, Once you get to Petersfield, I'd recommend heading west to East Meon, then down to clanfield then back on that purple line from Clanfield and you're set.
Like this :
http://maps.google.co.uk/maps?saddr=petersfield&daddr=East+Meon+to:Clanfield&hl=en&sll=53.800651,-4.064941&sspn=19.123242,39.506836&geocode=FdVECgMdzL_x_ymD4ggxijV0SDHYwQ-pqML7eg%3BFZAhCgMd60Dw_ymBs-udrDh0SDEjD6bDo8UmJw%3BFYBcCQMdEMDw_yldCvLUkEZ0SDE5zJdo4VuVmg&vpsrc=0&mra=ls&t=m&z=13
The other alterative is to head down through South Harting / Compton / West Marden and then through Havant then along the marshes.