I have suffered autumn hayfever, albeit not in Britain. In Britain, I sometimes get a bit of spring hayfever from tree-pollen, depending upon the weather that year, but that's all. The only other incidents have been abroad, and in the local autumn. The very worst I have ever had was one late October in Greece. I had no problem when on low ground among the cultivated fields, I had no problem when on very high ground in the pine forests. But at intermediate altitudes in the mediterranean shrublands, I was streaming. I don't know what it could have been as there was very little in flower. I have also been to Greece a couple of times in spring, and had no problem. I had a problem bad enough to be taking tablets in Patagonia in the local early autumn period (March). That was in the humid climates of the west coast - inland in the semi-arid shrublands it didn't seem to be a problem. Funny how things vary.

So, yes, there can be stuff in the air in autumn to bother people, depending upon weather and vegetation.