cambridge, of course have 'other' employers but, Cambridge
University was/ dunno if it still is though ? , the biggest employer there.... Oxford Uni employs lots of Oxford people ( Inc our own YF leader, @Eaststandboy ) ... but is nowhere near the largest employer in Oxford/ Oxfordshire - NHS and/ or Various car related manufacturing are probably the largest employers in the Oxon area ?
Here you go: https://cbselfstorage.co.uk/list-150-biggest-employers-cambridge-2014-2015/
The info I can access find for Cambridge Uni: https://en.wikipedia.org/wiki/University_of_Cambridge
Kier Group PLC is the biggest employer according to those. The list doesn't include the NHS which has a big presence in Cambridge as well with Addenbrookes Hospital part of the Cambridge University Hospitals NHS Foundation Trust which has similar research tie-ups as the NHS Trusts in Oxford.