This damned early winter is here also. My car is currently under a foot or two of snow.
Will post pics later.

Your problem is that the stuff you have in the washer container, at - 7 C it's frozen to ice.
As GB is not that used to these kind of winters im not sure if your gas stations sell
washer fluids that manages -10 C (I have -25 C stuff in my trunk) but if they have, go and melt your car somewhere (this may take some 12 hours) and try to get the wather out of the system in put in the winter washer fluids (5 liters).

I actually have the same problem. The early icy weather surpised me also

 

I have 100% pure -8 C washer fluid ... last night while driving the temp varied between +0.5C and -10.5C. Anything below -3C and washers wouldn't work.... after a sustained period above -2C they eventually came back. I guess the narrow bore pipes from the washer resevoir to the spray nozzles freeze up and that heating the actual nozzles can't solve this?

 

-10.5C? I need to remaind you of the wind chill fatctor. Frosen is frosen.

Get some -25 C stuff. Don't cost much at least over here. Some 3£ / 5 liters.

But first you need to get rid of the wather (100% pure -8 C washer fluid).

 

I've talked with my dealer and got this info regarding the windshield and headlamp washers.

The heater is only in the nozzle itself to prevent the nozzle to get clogged.

The washers should work in ALL temperatures. If you activate the windshield washer several times in a fast sequence the headlamps gets a spray every 7:th time. Headlamp washers are also time controlled, so if you pause activating the washers for a couple of seconds the counter is reset.

Even if the headlamp washers are frozen tight to the bumper there is no risk of damaging the mechanics. They are activated by the pressure of the fluid so if they are stuck or if there's no fluid they just don't pop-up.

 

Good info Scandic24, thanks. But your dealer is full of "BMW sermon" doctrines.

In my earlier BMW's the headlamps got a spray every 3rd time (what is a fast sequence?).

"Headlamp washers are also time controlled, so if you pause activating the washers for a couple of seconds the counter is reset." What does this mean?

"Even if the headlamp washers are frozen tight to the bumper there is no risk of damaging the mechanics. They are activated by the pressure of the fluid so if they are stuck or if there's no fluid they just don't pop-up." Where does the fluid then go?

Sorry to say but I doubt this. For example if the half iced headlamp washers may get up but not all down.
And what about the fluid pump. How many times does it function "dry" (i.e. with iced flusher fluid)?
The iDrive warns to use the windscreen wipers for the same reason.

The BMW theory don't impress much.

 

The windshield washer counter will increment by one everytime you activate the windshield washer in a fairly fast sequence. When it reaches 7 it will activate the headlamp washer. If you activate the windshield washer, let's say, 3 times and then wait for x no of seconds the counter will be reset and start from zero the next time you activate the windshield washers.
(It may not be 7 but that's not really important.)

As for the pop-up washers - it is true that they can pop-up but can get stuck on the way down due to ice and snow. There's a possibility that the small "lid" can come loose. If it gets stuck, just remove the ice and you should be fine...
If the pop-up lid is frozen stuck, the fluid will go back into the tank. Without a doubt, the pump has a return valve that will take care of that

I haven't seen any warning message for the washers in the iDrive...