No, I don't think so. Other universities have improved tremendously, particularly some Russel group ones, to the point where UCL and LSE are as good if not beter than Oxford/Cambridge at particular subjects. Overall though, the preeminence of both Oxford and Cambridge is reinforced by their alumni's dominance over evey aspect of British life (except Sport??) . Academically it can't afford to pay as much to its teachers, but academics are rarelly in it for the money. The concentration of great academics at Oxford mean more of the best academics are drawn to become part of it and live there.
Morover, Oxford and Cambridge remain the target of the brightest students in the UK and this influence is felt in other countries round the world - I have somebody in my year who rejected Harvard for Oxford. Its not always like this, ie. many undergrads prefer Ivies to Oxbridge, but the scope of this influence is hard to deny. Crucially it still eductes a disproportionate amount of world leaders in politics and other fields.
Oxford in particular holds more sway in America than Cambridge does, based on my own encounters with Americans as well as the preponderence of Oxford on Collegeboard forums. It is still the powerhouse of world thinking in the humanities, with a huge concentration of the worlds' formost historians, literati and political scientists. In the sciences yes I would agree there has been a more significant decline, simply because the resources are not available to compete with richer universities, nor does it have access to as huge a tech-base in the same way Stanford does with Silicon Valley. Cambridge however picks up a lot of any (slight) slack in science, esp. in Maths and Economics, so between Oxford and Cambridge together, they are pretty much untouchable at the apex of higher education. I realise this sounds arrogant, but it is difficult to refute.