I thought I'd do it online this year, so having selected my best quote, I
proceeded with it until I reached the page that required my credit card
details.

Next, perhaps in response to my hesitating at this point, a chat window
suddenly opened. I was thus conveniently able to ask my concern
that, if I continued and completed this purchase, was I also consenting to a
continuous charge authority against my card?

The reply was that, not only was I indeed consenting, but also further that
I could not withdraw my consent online. This could only be done later -
by phoning them after I'd purchased.

I told them I didn't like that very much and would defer my decision while I
considered it.

Can anyone tell me then if this method is industry standard?

(This was Churchill Car Insurance btw).