I don't think you would fail to get a TC simply because you went to Cardiff over Warwick.
I've been to a lot of interviews and assessment centres at London City firms and there do seem to be a fair number of Cardiff trainees at some of the best firms, but there are of course trainees from a whole host of other redbrick unis too, including Warwick. When it comes down to post-interview selection, I don't think they'd ever pick someone on the basis that they went to Warwick over Cardiff unless there was simply nothing else to differentiate them, which is unlikely once you've gone through an entire assessment process.