Reasonable enough to be accepted on the North Downs Line I'd think (TON-OXF is valid for instance) - albeit at your own risk. Going via London would be quicker though - changing at Oxford (same platform) is preferable to Reading in this case. Bear in mind there's only one XC per hour stopping at BHI (the Manchester-Bournemouth service).
I've noticed before that the North Downs Line is missing from some routes where it would be quite reasonable. In many cases the only option is via London - one would think that a cheaper Not London ticket would be attractive, even if journey times are longer.