After reaching Penton Hook, the author, J, and his friends decide that they will try to continue past Staines before they set up camp for the night. However, all of them soon come to regret their decision. They become lost, missing Bell Weir Lock, one of their landmarks. Soon, they pull in to Picnic Point instead of the intended Magna Charta Island and proceed to set up camp.
This frustrating experience reminds J of a similar situation he found himself in not too long ago. He describes being out with a female cousin on a boat. They had just come up to Benson's Lock at the time; it was to have been a mile and half to Wallingford Lock from there, and five miles from Wallingford to Cleeve, their intended destination. However, after they row past Benson's Lock, both become utterly frustrated when they cannot locate Wallingford Lock. J's female cousin opines that they 'should both be drowned' and that they would never reach their destination.
They are saved when they hear a boat approaching their position. J can hear the sounds of singing and the music from an accordion. Both are greatly relieved when they are told that Wallingford Lock doesn't exist anymore and that they are actually quite close to Cleeve.
As for whether the accordion was the last hope of the author and his cousin, one could say that it did provide J and his cousin some much needed relief during a difficult moment. The people on the boat confirmed the author's position close to Cleeve, the intended destination, which greatly encouraged J and his cousin to persevere despite their exhaustion. The accordion (and the people on the boat) established that they were not alone and that they were on the right track, a great comfort when one is lost, exhausted, and at the end of one's courage.