1. If it whirs all the time, the motor is running, so replacing it is not likely to do anything.
2. If the outside metal cover has a small raised bump in it, then it is one of the later valves, in which the actuator mechanism can be changed without affecting the water side.
3. Try:
3.1 Isolate the electrical supply to the valve. Unless you know how to test for live power, and have the equipment to safely do the test, I'd recommend turning the whole house supply off at the consumer unit.
3.2 Remove the outer metal cover.
3.3 Slacken the two screws which secure the actuator assembly to the actual valve part. The valve part has a brass base.
3.4 Jiggle the actuator mechanism around a bit, then re-fasten it.
3.5 Replace the cover and reconnect the supply.
3.6 Test to see if it now works.
4. If it doesn't work, replace the actuator:
4.1 I'd buy a replacement valve, the whole thing, not just the actuator. The price difference is small.
4.2. Isolate power as above and remove old valve cover.
4.3. Remove old actuator.
4.4. Check the spindle of the actual valve. It only moves through about 20 degrees, but you should be able to turn it with your fingers, or at worst with very light pressure from a pair of pliers.
4.5. If the spindle doesn't turn easily, replace the whole valve. See 5. below.
4.6. Remove new actuator from new valve and fit to the old valve base.
4.7. Replace the valve cover.
4.8. At the wiring centre, or equivalent, identify the 5 wires from the old valve (brown, blue, yellow/green, grey, orange) and cut them about an inch from the wiring centre terminals, leaving the insulation in place. It is best to make a note of all connections in the wiring centre, as these can be very confusing.
4.9. Connect the wires from the new valve to the terminals in the wiring centre, colour for colour, removing the stubs of the old wires at the same time.
4.10. Test.
5. If you have to replace the whole valve:
5.1. Drain the system (radiators and hot water cylinder) to just below the level of the valve to be replaced. If you have an F&E tank (in the loft?) empty and clean this out first, otherwise you will wash any rubbish in it into the radiator circuit.
5.2 Undo the compression nuts securing the old valve in place and remove it. You are likely to get residual water, so lots of old towels.
5.3. Insert the new valve (complete). Provided you are swapping Honeywell for Honeywell, you can re-use the old compression nuts on the pipes and the old olives. Best to use a little jointing paste (Jet Lube V2) on the old olives. If you want to use the new nuts and olives which come with the valve, remove the old olives and nuts first. You shouldn't then need any paste.
5.4. Do the nuts up finger tight, then 1/3 to 1/2 turn with a spanner. If you have a slight weep on refill, nip the nuts up a little more but don't overdo it.
5.5. Connect the new valve's wires into the wiring centre as 4.8 above.
5.6. Refill the system, checking for leaks as you go.
5.7. Test