That's why when conducting any financial transaction you have to obtain and maintain your proof otherwise, in the words of Judge Judy, it doesn't exist.
In the case of online transactions, always make copies or screen prints and keep them in a special folder/directory on your computer. So should anything go wrong you can email your proof back to the charging organisation.
Sorry to hear this, I have had the exact same issue, which lead to me being charged for 5 months for a service that I never used!
After realising four months in, I got in contact on the live chat, and they offered a partial refund, and said they had cancelled the subscription themselves, and then a month later I realised they still had not cancelled it!
However I was able to obtain a full refund. This came after a lot of persistence, and involving a manager in their live chat system - at first two live chat team members insisted that the best they could offer was three months reimbursement.
My advice would be to not take no for an answer in this scenario, since the way they go about the cancellation process is unacceptable.