The answer is in a couple of parts really. Cambridge University is made up if 31 colleges, which were established as far back as the 1300s, right up to the 1960s. I would guess its a little like the Frat and sorority houses in US Colleges (if there are several to a college). Cambridge University itself has the colours of blue and white, the blue being a light blue which actually is known worldwide as Cambridge Blue! Coincidentally I designed and ordered some scarves for my own School Old boys association about two months ago, the colours being Cambridge Blue and Myrtle Green (like a bottle green) with the addition of chocolate brown for the Old Boys Assn. So your scarf isnt a University scarf, although saying that, the university didnt actually have one until the 1990s, and then permitted a cambridge Blue and royal blue one.
The individual colleges all have their own colours, some several hundred years old. However, of the 31, I dont see any that resemble yours, the nearest being Girton College, although their colours are bright green, with red and white stripes.
The nearest seems to be Royal Holloway, part of the University of London. Their scarves are dark green, with mauve and white stripes. See https://epay.rhul.ac.uk/store/shop/products.asp?func=prod&compid=1&deptid=9&prodtypeid=6
and scroll down. Another candidate might be St Aiden's College, Durham university, which is the same, but with red stripes.
Experience with the scarves I have in the school archives shows that after sun bleaching and washing shades can vary greatly. Also the different manufacturers of rugby shirts, ties and scarves all have slightly different interpretations of colours. Unfortunately, with many Universities, and Public, and Grammar schools, it might be anything. Trouble is many of the schools no longer exist, so it might be impossible to confirm.