The purple hairstreak is quite common in oak woodland but that does not mean you will frequently come across them. They are small, dark coloured butterflies that spend virtually all of their time in the upper canopy of oak and ash trees and rarely come to our level. They feed on the honeydew produced by aphids and so do not visit flowers hence their high level living. The books say they fly from late June through until early september.
Here in Dorset the weekly reports chart shows emergence in week 25 which is, indeed late June, and then there are weekly reports through until week 33 in early September; the Dorset purple hairstreak is a textbook species! Most reports come early in this flight period in early July.
There are reports from twelve Dorset sites so far with Alners Gorse producing the most. Given the dependency on oak trees a couple of the sites listed, Radipole and Lytchett Bay, are a little bit of a surprise to me. However, true to the book again, all nineteen sightings in the Nature of Dorset database for 2017 and 2018 come from sites where there is a degree of broadleaf woodland present and broadleaf woodland almost always features some oak.