Hello, my name is***** am a qualified lawyer and I will be assisting you with your question today.
Do you have copies of the cancellation email you sent that you can use if necessary?
Did they specify in the terms an email to be used for cancellation?
If they simply stated you must cancel by email and did not provide a dedicated cancellation email, you should be able to argue that you have cancelled as per their terms because you did after all send an email to one of their recognised email addresses.
Also they did indeed cut off your services at the start which meant you could not use them and whilst that may not automatically exonerate you for the full amount, it would at least give you a good chance to argue a discount.
Finally, they are a German company, you are a UK individual. To force you to pay anything they have to take you to court and win. The amount is a rather low £100. Considering the complexities involved in cross-country claims, I very much doubt they will ever go as far as suing you over this. They may pursue you now and make threats but in reality these mean nothing because only with a formal court judgment in their favour can they force you to pay anything. Even if they make a claim you would have reasonable grounds to argue you are not liable, or that the total amount should be reduced.
You can stick to your guns and refuse to pay and let them take this further if they want to, which as mentioned in reality is unlikely.
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