The law regarding the MoT certificate, proof of insurance, and driver's license is rather curious. There's no law which says you must have them with you in the vehicle at all times, but there is an act which makes it an offense if you cannot produce them on the demand of a police officer. So strictly speaking, you're breaking the law if you get stopped and can't show them.
As Dennis pointed out though, in practice all that happens is that you're given a "producer" ticket which lists the documents you need to present at the local police station for inspection within 7 days. So long as you show up with them within the required time, nothing else will happen. (If you don't, of course, then you can expect a summons to follow in due course.)
The vehicle excise license, or "tax disc" as it's more commonly called is a different matter though. The law requires you to display a valid tax disc on the left-hand corner of the windshield, or on an adjacent side window (e.g. if you have an older-style quarter-pane vent on the door) at all times when the vehicle is on a public road (even if just parked).
I normally carry the MoT certificate, registration, and proof of insurance in my car all the time anyway.