This is a question to which the answer is rather more complicated than a simple "you must have" or "you need not have" if you want the full picture.
It's widely believed by British motorists that there is no requirement to carry any documents with you in the car (except the tax disk, which must be on display, of course). That's true to an extent, but it's not quite that simple.
There is no specific legislation which says that you must carry your license, proof of insurance, etc. with you when driving. So in the strictest sense, you are not obliged to have any of them with you. However, technically, you commit an offense if you are unable to produce any of those documents upon demand to a police officer, which means that you would need to have them all with you at all times in order to avoid the chance of breaking the law if you happened to be stopped.
However the law also states that it "shall be a defence" to such a charge if you produce the required documents at a nominated police station within 7 days. So although technically you might have broken the law if you cannot show your license etc. upon demand, in practice all that happens is that the officer will give you a ticket which requires you to turn up at a police station within the required period. So long as you do so -- and all of those documents are in order, of course -- then the matter is closed and no further action taken. If you don't show up, then it would be referred to be considered for prosecution.
Until very recently the above would have covered everything, but unfortunately there are now further considerations with regard to proof of insurance. Police officers have been given powers to seize vehicles from drivers they have reasonable cause to believe to be uninsured.
Unfortunately, some police forces and individual officers are exceeding their authority and trying to seize vehicles from people who cannot produce proof of insurance on the spot, or prove cover by other means, even though they are not allowed to do this. So today, it's probably a good idea to make sure you carry your insurance certificate in the glove compartment, just to avoid any problems if you happen to run into one of these gestapo agents who are misapplying the law. At least you should keep a record of your insurance company name, policy number and so on in the car so that checks can be made easily at the roadside.