Great, thank you. I didn't realise costs could be awarded, but in this case I believe it would be justified as it is spurious for them to reject. I was pretty close to just paying the £65 and move on with my life, but the solid case (reiterated by you!) meant I decided not to pay.
Yes I will appeal to London Tribunals and will include the text you shared.
While researching the original appeal letter, I noticed on the London Tribunals search page that I couldn't find any cases in Greenwich for my location. I suspect the cases aren't registered properly as I find it surprising that have been appealed.