If you fit that bill I’d strongly advise you to get in touch with Grads Kent. They are very keen on talking to those grads in Kent now looking for graduate level work in Kent. The value add they bring is that they aren’t a recruitment agency so have a slightly different motivation about what they’re trying to achieve and they are spending a lot of time with local employers encouraging them to recruit at graduate level. So if you don’t see a vacancy on their website that matches what you’re looking for tell them what it is you’re looking for and they will proactively try to find it.
Don’t live in or want to work in Kent? How about seeing if something similar exists in your area?