the best accounts in English language are CV Wedgewood: The 30 Years War, and a couple of books by Geoffrey Parker. I think there is a more recent one but havent read it yet. Parker and Wedgewood should be available at your local bookseller they are still in print. Wedgewood was writing about 60 years ago but she's very good and goes into much of the battles. Parker is more about the political dealings, alliances, religious edicts etc.

The English were trying to support Frederick V; the "Winter King" he had married one of James I, king of England's, daughter. He was the elector of Palatinate but they elected him King of Bohemia, to foster some sort of protestant alliance that sort of began this war. of course the Protestant army was crushed at White Mt. in 1620 and his reign never really got going.

There were various English and Scottish guys who fought as mercenaries. Munro was a scottish officer who served under Wallenstein for the Catholics, but there were various english mercenaries serving on both sides. I forget the names.

I dont think there was much more english influence other than that. At first the english were promoting the Winter King early in the war. then about 1625, the Danish led by Christian of Anhault as well as Saxons led the protestant alliance. Then Gustavus and Swedes led the protestants and finally the French. so I dont think the English influence lasted very long in this war.

Eventually the civil war in England took precedence, that was about 1640.