Cambridge University's Fitzwilliam Museum is free to enter, and with famous 19th century European artworks, Egyptian mummies, and vast collection of ceramics, it's got plenty to see in a relatively small space.
When it comes to dining, there are a few traditional -and tasty- English places to eat, including Fitzbillies Bakery and The Copper Kettle on the Market Square. While in Cambridge, a session of punting on the Cam followed by a pint in a riverside pub is essentially obligatory.
King's College Chapel is the undeniable architectural gem of Cambridge, and if you're willing to queue up on Christmas Eve the televised Carols from King's service is free to enter for the public. As for transport, if you're staying any length of time then a bike rental is an excellent idea.
Trains to Cambridge run extremely frequently, with the "Cambridge Cruiser" reaching Kings Cross in just 45 minutes, meaning that the quaint fenland city is easy to reach on a day trip from the capital. Trains also run to Liverpool Street.