I don't know about this service station, but we once overnighted at one on the M4, never again. I see that this is not a million miles from Godwins Ice Cream Farm just off the A34, just south of Bicester, you could try it instead. You could then continue on the A34 I think, as it goes to Winchester.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.