Enter your journey details into the National Rail website and it will offer all recognised routes. (It's important to find an official 'recognised route' because those routes allow you to book through fares. Alternative routes might require the purchase of several separate tickets, which could be far more expensive).
The principal route (other than via London), which is offered by the NR website, involves just two changes, at Winchester and Birmingham. Journey times are roughly the same as travelling via London.
The single fare is �70.50. (There also seem to be a very limited number of trains where there are cheaper advance purchase single fares available). The return fare is �141.00 without any restrictions on travelling times, or �87.10 when travelling off-peak.
http://www.nationalrail.co.uk/
Alternatively, if you simply wish to avoid the underground (rather than London), the number 168 bus offers a frequent direct route between Waterloo and Euston.
Chris