Is it both hot and cold water, or just one line?

Probably doesn't make any difference, though. It sounds like a failed solenoid problem (though having both run would make me think it's a problem closer to the central electronic brains which would be more complicated).

Anywho - the water supply lines are controlled by electronic devices that tell them to turn on/off for certain predetermined periods within the selected cycles. It sounds like one (or both?) of the lines has got itself stuck in the ON position. It could be something simple enough to fix by just deconnecting and reconnecting the connectors, but it may be a busted solenoid that will have to be replaced. Doesn't sound like a big job - I know we would tackle it ourselves. The tricky part would be figuring out which part to order. Miele parts are not cheap, though may be more reasonable in Canada. Shipping/handling directly from Miele in the USA is extremely pricey. OTOH, you can (with a little effort) get through to very knowledgeable c/s people who will help you get what you need. I usually have to been a bit persistent about not wanting or needing a service call, but it's not hard to get beyond that, well, most of the time.

The good news is that the machines are quite easy and straightforward to work on - the Miele value of highly rational mechanical design is a joy to work with. A word to wise on Mieles: if what you think should be coming apart doesn't do so in a pretty easy way -STOP! You may be doing it wrong.

Identifying and getting the right part shouldn't be too hard. IIRC the solenoids and electronic water controlling harness are are easy to access. I have a 1986 apart in my garage right now and I can check tomorrow to see if you have to open the front to get the top off, or not. (I only opened it up a few months ago, but I'm sorry I've had other things on my mind lately and I can't quite recall.) The part may be a bit pricey (not this part in particular, just Miele parts aren't cheap!), but I don't think it's a death knell for your machine. Once fixed, it should go back to work for a long time.

It must be awfully hard to spin your clothes dry with the water running!

HTH.