That said, someone applying for a postgraduate degree at Oxford who did their undergraduate degree at, not TVU, but somewhere like Lancaster or Aberdeen, perhaps, will have their application looked at with equal consideration to someone who did their undergraduate degree at Oxford. Where the comparisons are strictly academic, it is very possible for a bright, hardworking candidate from a "lesser" university to get into a competitive MA or PhD course.
But there are some employers who don't care about or realise this, and there is still a bias towards graduates from Oxbridge and traditional redbrick universities over graduates from new or ex-polytechnic universities. This is more the case for very competitive graduate-entry careers such as investment banking or law, where you don't need to have a degree in any particular subject. If the subject of your degree is irrelevant, the institution probably won't be. That is why a degree in English literature from TVU won't be worth much, whereas a degree in something really specific from TVU might well be much more useful, because TVU could be really good at that certain niche course, but it sure as hell isn't for a traditional academic subject.
To be honest, once you've been working for several years, your degree will become irrelevant, as your working history will be much more important to future employers. But for the purposes of getting onto that career ladder in the first place, you'd be doing yourself a favour by going to the best university you can get into for your particular course.
However, it doesn't make sense to go to a slightly better university you don't actually like the look of above a slightly lesser one you love. Happiness counts for a lot, and unhappy people don't tend to do as well in their degrees as happy people. Employers will also be interested in your extra-curricular activities, not just your degree, so it's important to pursue lots of different things during your time at uni.
In short, it is better to go to the best university possible, especially if you think you might want to do something highly competitive afterwards, but personality, work experience, extra-curriculars and the like all matter too. And I think a first is bloody impressive, no matter which university you went to.