Complete Save can't take money out of anyone's bank account unless they've been provided with the account details. You must have clicked on an offer on one of Complete Save's partner companies websites (which, apparently, does include The Trainline.com - but there are hundreds of others) and failed to read the small print.
They're a Swiss company, so (if they fail to pay up) you might have difficulties pursuing them for your money. (Good luck!)
Incidentally, if you do buy rail tickets online, you should NEVER use third party websites (such as TheTrainline.com). They can't offer cheaper fares than those available through the National Rail website, they frequently charge MORE (through adding on a transaction fee) and they've been known to issue tickets which aren't valid for travel on any train. (I used to run a railway station and had to sort out lots of problems with their tickets). Go here
http://www.nationalrail.co.uk/
(or the website of the relevant train company) and nowhere else!