From my point of view, the old guy is being perfectly responsible and polite with it, He clearly has a lot of time on his hands and most of us have "budget challenges" he has ever so slightly over rated the £21 per annum increase, and in the cold light of day it looks a bit petty, in an attempt to justify his objections he has "shown you his workings out", The response is worded so that its not an outright "Dont come again" letter ,nor a complaint about the service, more a " I have been a good customer can we just remain at the old price" notice, Even if this tactic didn't work and he had to accept the price rise it had the secondary effect of making you more cautious putting him up in the future,
In the past when he was more busy. I am sure the price rise, would have just been something he accepted without concern, now retired he is more concerned with the house outgoings.
FWIW. I think your response pretty much nailed it, you couldn't just back down, so you gave him the same "Show me your workings out" respect that he offered you and with the length of it, he would be assured you have considered all the options,
Thus respectfully, letting him know the price is the price for the service and IYHO a fair price at that.