Aircraft airworthiness can be broken down into two basic parts. What's legal, and what's safe. Both must be satisfied in order for an aircraft to be considered airworthy.
To be legal, an aircraft must be in conformity to it's type certification, modified type certification (by a supplemental type certificate), or by another manner which has been deemed acceptable and legal. Certain operations with inoperative equipment addressed by a Minimum Equipment List, Configuration Deviation List, or other such means are one such example. Some aircraft manufacturers publish in the aircraft operating handbook a list of installed equipment and guidelines as to what must be functional and what can be inoperative and still be in compliance with the airworthiness certificate.
When an item is inoperative, a general guideline is that it must be deactivated, and the means of doing this vary with the equipment and the regulations under which it's operated. This may mean pulling a circuit breaker. It often means placarding the particular item as inoperative. It may mean deactivating or placarding a control...and it may require the signoff or attention of a mechanic (engineer).
Once the legality of the item is satisfied, then one must also ensure that the change is unsafe. One may be legal to operate without flaps, for example, but given the nature of the flying one undertakes (short, slick icy air field, for example), one might not be safe to operate without the flaps.
Your stall warning is inoperative...but are you safe to operate that way, and are you legal to do so? Is the stall warning required by the type certification of the airplane? How do you know? In a nutshell, you should have an equipment list or a furnishings list in the aircraft flight manual, and this will list everything put aboard during certification and production. You may find this in the weight and balance section of some airplanes. If it's part of the aircraft as certified, then it needs to be installed and functioning, or some other form of relief must be provided. Once you've settled the question as to whether you're legal, you need to determine if you're safe.
This really depends on the airplane. You may be flying an airplane which provides ample physical indications of a stall, and can fly just as easily without the stall warning. Or you might be flying an airpalne which simply quits flying and rolls over on you...some do that, and provide precious little warning about a stall. Do it in an accelerated conditions, such as in a steep turn, and you may find that it doesn't take very much lack of coordination on the rudder, before the airpalne rolls out over the top or tucks in underneath and bites you. In this case, you may find that operating with the stall warning inoperative isn't safe.
Remember, it has to be safe and legal to go fly.
I don't know about the UK regulation, but the US regulation spells out exactly what minimum instrumentation is required for a particular type of operation. This may be day VFR, for example, or night IFR. This requirement is entirely independent of what the specific airplane may require. That is, you need to meet the requirements of both regulations...both what the aircraft certification requires, and what the FAA or CAA regulations require. If you're flying an aircraft of a different nationalities registration, then you may need to be in compliance with multiple types of regulation.
It's important to realize that when you're handicapped by inoperative equipment, you are also subject to much bigger handicaps if something else goes wrong. Some of it may surprise you...you need to play a game of "what if" with yourself to determine not only the ramifications of the inoperative instruments or equipment you have now, but what you might have if something else fails...and plan for that as well, in order to be safe.
For example, I fly a multi engine airplane that uses hydraulic pumps. It's got redundance with engine driven pumps, air driven pumps, and electric pumps. If I've got an air pump out, then I've still got the others. Not too long ago I left Sheffield airport (I think...Robin Hood field, was it?), and had that very problem...one of the pumps split a case. We deactivated it...now it was legal. However, if the other pump failed, we'd lose our ability to raise our landing gear. If that happened then we also had a reduced climb performance. It also meant a flap problem if we had to come back and land, so we had to consider our increased landing distance, and so on. More than meets the eye...you may have more impacted by the loss of a vacum pump, for example than you think
A vacum pump...so you lose your instruments. It's day, VFR. Not a problem. But you're enroute, and have to divert, and suddenly it's getting dark. You'll get back before dark, but today there are a lot of clouds forming on the horizon, and they cause it to get darker sooner, and now you're looking at flying home on a tipped attitude indicator, a failed turn and bank indicator, and a heading indicator that continuously gives wrong information. This by itself might not be a problem, but couple the fact that you don't have the useable instruments to the fact that you have instruments giving misleading, false indications, and you could have a dangerous situation.
The battery starts to die enroute. You can fly home becuase the engine will keep running with or without the battery...you know this. You also know if you land you can always hand prop the airplane...so getting from A to B shouldn't be a problem. However, do you know why the battery died? Do you have a short somewhere that could turn into a fire? What if you have an engine failure and need that battery in flight to restart the engine? What if you have an emergency that requires the use of the battery to operate a radio? How about lowering landing gear, or operating lights or a beacon, should it develop into the first situation...diversion, getting late, getting dark...etc?
You can see that a simple problem can compound itself shortly...the inoperative item itself may be the least of your worries, particularly if other factors develop. Look not only at the inoperative item and your planned flight, but at the inoperative item and the unplanned things that could complicate your planned flight. This is part of the "is it safe" equation in the two part decision regarding airworthiness.
It's always two things: is it legal, and is it safe? Unless the answer to both those questions is a resounding "yes," then the flight should not be undertaken.