I have just bought a flat, three-story block of flats in Cambridge.

All of the internal doors are fire doors which I understand is a requirement. But all of them are fitted with a self-closing chain (see attached image).

Currently the property is a private dwelling (I occupy it). But in future I will likely rent it.

So my question: What are he UK requirements for internal doors in flats? Can someone point in the direction of the guide lines/requirements

I would advise you to consult the following local government document on this subject....."Fire Safety in Purpose Built Blocks of Flats" at https://www.local.gov.uk/sites/default/files/documents/fire-safety-purpose-built-04b.pdf 

Edited July 22, 20196 yr by Neil ashdown
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For decades in the past  it was a Building Regulation requirement for certain  internal doors in dwellings (especially flats) to be self closing fire doors, but for a long time now that requirement has been removed and they just need to be fire doors. Most of the time the chains were cut or doors propped so it was considered pointless and better to allow free swing and educate to close at night.

Looking at the door it has brass hinges which are not fire rated and pretty useless in a fire. 

Page 19 of the document 'Code of Practice:  Hardware for Fire & Escape Doors' at  http://www.firecode.org.uk/Code_of_Practice_hardware_for_fire_and_escape_doors.pdf  provides guidance.