I do Cambridge to Filton from time to time.
The route you're looking for is WCO Q41 NORRY L9 MALBY DCT OF.
If you're simply doing this for the exercise of flying IFR on airways, fine. But it's FL100 for a 35 minute trip in a light piston-engined aircraft. There are three options, of which that's one.
Operationally, I would recommend a simple direct routing at lower level, getting a traffic service from Brize. In my experience, handover to Filton is seamless. There's a slot in the Daventry CTA at FL60 if you need it, and pay attention to Hinton and Weston. You can also fly a similar route low level VFR.
My preference depends upon the weather. Mid-level IFR is the default. If there's significant low level turbulence or icing expected at those levels, I'll go airways. If there's summer convection, with high bases, I'll go VFR below it -- it's easier to avoid the worst of it that way.