The OP is most certainly entitled to either their costs, or the "overpaid" fare. The TOC is not legally permitted to fail to provide the service and yet refuse appropriate reimbursement!
The problem is that the OP is highly unlikely to be able to show that he incurred any costs. Unlike taking a taxi, where you produce a receipt to prove that you both made a journey and paid for it, how does the OP demonstrate that he actually drove in his own car to the interchange station? As opposed to say getting a lift with someone else. This is not the same as claiming mileage expenses, where there is prior agreement not just to make the journey, but in what class of car. Whilst it would be nice to think that, should I choose to use my chauffer-driven Rolls-Royce in a similar situation, that I would get the costs back, I somehow doubt it. Especially with nothing to show that I actually made the journey at all, let alone in a Rolls.
The overpaid fare may be zero. For example, the fares from my local station are the same as those from my interchange station. So if I were to do the same, the difference in fares between the journey made as opposed to that paid for would be zero.
Given FortheLoveof's requirement that the TOC should either pay the costs of my Rolls journey or reimburse my zero fares difference, I know which option I would choose if I were the TOC!
I certainly would not recommend claiming delay repay as standard, as others appear to be suggesting. Claiming for a delay that you did not actually incur would be fraud, and could carry serious consequences if detected. On the other hand, explaining what you actually did, and suggesting that the TOC should pay the same amount as you would have been entitled to had you waited for the next train, to help defray the costs that you incurred, would be entirely legitimate and reasonable.
Unfortunately the delay repay compensation may also be fairly insignificant, depending on how long the delay would have been and how much the tickets cost. For example, for a delay of say 58 minutes and cheap Advance tickets, the compensation may be fairly small. Certainly compared to what the OP may have paid to park at the interchange station all day. So, in my view it would also be reasonable to request any parking charge be refunded. Especially if the fee were paid to the same TOC as the cancelled train, as the TOC should not financially benefit from the OP as a consequence of their cancelled train.
My opening gambit would be to request whichever is the largest:
* the difference in fares
* the compensation that you would have been entitled to had you waited for the next train
* the cost of a return from your local station to the Interchange station (the journey you didn't make by train)
to help defray the costs of you driving there and back, plus a refund of any parking fee that you may have paid (supported by a receipt if possible). When they respond, the minimum that you should accept is the compensation that you would have been entitled to had you waited.