Radio
The UK has many outstanding radio stations. BBC Radio 4 (99.3 FM or digital audio or iPlayer) carries news and more intellectually-oriented programming. BBC Radio 3 has classical music with quite a bit of talking about classical music.
TV
In addition to many broadcast TV channels that can be picked up using a standard antenna, the UK has
(a) FreeTV, which is a digital set top receiver that receives HD TV stations and is free
(b) FreeSAT, which is like FreeTV in that it is digital, but requires a special receiver (or high-end TV) that can be connected to a satellite dish
Streaming TV is available from the major TV channels (BBC, Sky, Channel 4, etc.). Some of it is free but has advertising. BBC does not carry advertising, but watching BBC on iPlayer (or even over the air) requires an annual license fee (about £170/year). If you access BBC content without a license, you are liable to a hefty fine.
Theatre
Cambridge has many venues that feature live performances, mainly during term. Most fences in central Cambridge are plastered with adverts for shows and are worth a quick perusal.
Bookshops
Cambridge is blessed with two huge bookshops: Heffers and Waterstones. Numerous smaller bookstores include G. David, which has been around since 1896 and sells used and antiquarian books and the Haunted book store. The local Oxfam and other charity shops also have extensive (and inexpensive) collections for sale.
Libraries
There are more than 30 excellent libraries in Cambridge, though admittedly many of them are private college libraries that are not generally open to the public. The University Library is massive and receives a copy of every book published in the UK, which it (somehow) stores in its cavernous depths. University members may enter and browse the books (sans backpack, which must be stowed in a locker). Some books are only available in the reading room.
Magdalene college has Samuel Pepys’s library, which is a gem and worth a visit.