It would need to be limited (very) stop to attract pax▸ onto the long distance service. No good if its quicker via London... The other stops would need to join their local service & change where necessary
Chippenham to Bedford via London - 2 hours and 40 minutes (160 minutes) - from journey planner for tomorrow
Chippenham to Bedford via Didcot and Oxford - 1 hour and 40 minutes (100 minutes) - Journey planner to Oxford and then East / West rail projections.
Even if you add in Royal Wooton Bassett and Wantage stops, I can't see it being slower via London. And you could save 10 minutes by taking out the reversal at Didcot.
Note that I've taken a worst case example - journeys to Milton Keynes will make a higher proportional gain. ChrisB - can you give us an example of a journey that would be slowed?