Seeking self-contained weekday rent for mum & son

Together with my son, I am looking for a Monday to Friday (or 7 day), self contained place to rent. We'd like somewhere with a kitchen/kitchenette, private bathroom and private living space. I am 49F, a senior manager working for NICE, an arms length body in health. My son (16M) is starting hiss A levels at a specialist maths sixth form in Cambridge, and we need a place to stay during the week for the next 2 years
(but will consider a shorter period). We will commute weekly from our home in Milton Keynes during school term times, arriving in Cambridge on Monday mornings and leaving on Friday evenings. For the budget stated, we'd like a place where bills are included.

We would consider furnished or unfurnished places, and will need at least one separate bedroom, and space for two beds (or one bed and one sofa bed). We'd also need space for a desk, and good WiFi (as I will be working remotely). We'd like to be within easy commuting distance of Mill Road/Cambridge train station, by bus or train, or walking.

We are both tidy, responsible and respectful people who take care of our own family home, and would look after our weekday home foo. My son is quiet and well behaved, focused on his studies and is a proud geek! We love cats (but we would not be bringing our own!)

Happy to consider any self-contained space such as a one bed flat, garden annex, or large loft room/suite. We prefer not to share a bathroom, kitchen, or living space with others, but we are friendly and easy to get along with if sharing any outdoor space, shared entrance or similar. Ideally we'd like a parking space, or good on-street parking nearby. Thanks for reading.