Well, census data is available, and it's not just about how many people have come from overseas to live in the UK.
There's actually a section on the labour market. Now, obviously the data is not terribly detailed just yet, but there's some interesting information available.
Table KS501EW tells us that in England and Wales, 27.2% of the population aged 16-74 has a degree or equivalent - or higher. This is not exactly 'everyone has a degree nowadays' - although it does mean we have just over 12m people in the country with some kind of HE or equivalent qualification.
What makes this more interesting is Table KS608EW, which shows us that 40.9% of the working population is employed in occupational classes (from SOC) 1 to 3, or, what we class as 'professional employment' in the Key Information Set and on Unistats. These are, basically, what we now term 'graduate jobs'.
Does this mean we have too few graduates? I'm not sure - obviously everyone currently in professional occupations is not going to retire tomorrow (I've got a mortgage, for a start), and also we should not see the professionals as being solely for graduates. But it does reinforce the idea that we have a pretty high-skills labour market and that therefore we need a high-skills workforce. It's not exactly a new idea, but this is just one more piece of evidence showing how important our universities are.