Looking for Accommodation From December

I'm Eve, a PhD students in education at University of Cambridge. I'm looking for place nearby the railway station or botanic garden. I'm a quiet girl from China and I used to take a gap year in Europe. I get along with different European families. I live with host of families so I would hope to find a place to spend the Christmas and if possible also I could extend to end of next June and my budget it's up to 700 pounds per month. so if you know any place I could move in on or before six of December I would be greatly appreciated