There's likely another reason for this...
There is another reason why his family might want his ashes interred in Westminster Abbey and it's very simple: Hawking had a large following of very strange people and a public grave in a Cambridge cemetery (there's one off Huntingdon Road that contains the remains of other high-IQ individuals), containing his intact body, would attract these people and it would turn into a ghoulish shrine. Think selfies, inappropriate behaviour, perhaps some crackpot with a spade. At the end of the day, Stephen Hawking was a brother, husband and (grand)father who deserves peace and dignity in death.
Westminster Abbey is much easier to secure and in some ways a bit more discreet. There can be plenty of public tributes and memorials to Hawking, but his final resting place is nobody's business. The fact that he's interred alongside other scientists is a fitting tribute in itself.
And contrary to popular belief, Hawking wasn't an arch-atheist at all. I doubt he would have complained too much at the prospect of being interred in a religious building.