Not as many as you would think. The joint FGW/Thames Trains service around 2003/4-ish didn't seem to have that much custom.
That was an infrequent 75mph service and did not go past Oxford. It did not run for long enough to build a clientele before it was abandoned as the stock was more usefully employed elsewhere. It is odd to read on a pro-railway forum that based on 15 year old evidence rail services between these places are not needed.
The market area being addressed by the Go-Op proposal makes travel across the radial routes from London easier on an axis which is not currently well served. There are similarities to the suggestions from East-West Rail for services which essentially connect the area south west of Bristol and South Wales to Swindon, Oxford, Bletchley (for Milton Keynes), Bedford, Cambridge and Norwich/Ipswich with all the connections possible at the interchange stations. The difference is that the Go-Op proposal is not dependent on the construction of a railway.
Few passengers will travel end-to-end - it will be more akin to CrossCountry with passengers making a series of overlapping journeys.
The question is whether the number of potential passengers will cover the operating costs including the infrastructure levy and whether the operation will be sufficiently capitalised to absorb the start up costs.
What's not to like? The DfT would never have come up with such a suggestion and no taxpayers money is at stake.