I would push back on this. I dont tend to enter such a fray, but Bristol was and is seen as being on par with the London Unis and Durham. Maybe in the hyperbolic universe that is TSR, where nuance is lost on many, some Unis are seen (read deemed) to be inferior to others, but in the real world, the difference is negligible for all of these Unis, except for a small niche of entities, and in those circumstances Oxbridge is king.
Notts is generally on par with Durham, Bristol et al. More important it will get you where you want to go, similarly with Durham, Bristol, UCL etc. and the end result will generally depend initially on your degree classification to get you past the first hurdle, then overall fit (with the employer).
In full disclosure I am a Bristol Grad who graduated in 2012.