Had I have walked from Warwick station I would have been back home by 23:45. Thus my delay was 30minutes by that metric (I got back about 00:15).
I think you'll find that your "about 00:15" was logged as 00:14, so no delay repay is payable.

Had I not taken up the offer of a taxi I would have walked - that would have gotten me back about 00:30, a delay of 75mins.
I don't think you could voluntarily choose to delay yourself further AND claim compensation for it.
So there's about four different metrics that can be used (the fourth being - arrival time at Leamington (~57mins). Which is "correct"?
I already told you which is correct (as did GadgetMan), however you and the taxi driver came to an agreement to drop you off by your door.
I think that if your house was short of the station, then it would be fair to give that as the equivalent time you arrived at the station, and that's just your good luck (this time). If your house was further, then I really wouldn't advise claiming at all, or if you do claim, then at least take off the additional estimated taxi journey time.
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So a taxi (which is supposed to drop you at the railway station which is the end of your contract with the TOC) takes you direct to your door and you are still complaining/trying to get your money back!
Some people are never satisfied!
Indeed, threads such as these are not a good idea in my opinion, it often backfires on the person asking the question. I think
orpine is just curious, and wouldn't make the claims suggested (eg. for a 75 min delay) but the posts are certainly open to interpretation as to the motives.