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When Steed has to fight against his opponents, it often results in ruffled hair, damaged deposits, battered bowlers, torn jacket sleeves, a sweaty, and dirty John Steed.
Jodiff's former Steedophilia site has a vast collection of "Favorite Mussed Studly Moments." They're no less than 22 examples for situations with ruffled Steed during series 5, the Emma Peel season. Fortunately, that excellent site still exists due to the Internet Archive.

But series 2, 3 and 6 and The New Avengers also have their "ruffled and tousled" highlights.

Series 4 and 5: Favorite Mussed Studly (Steed) Moments from Steedophilia.
Ruffled and tousled moments from other series:

Series 2:

Warlock: Steed has to fight against black magic and a German Shepherd.

The Sell-Out: John Steed gets knocked out from one of his superiors and is a bit stunned afterward.

Propellant 23: Steed has a stiff neck and a cut on the eyebrow after a fight with an East-German agent.

The Mauritius Penny: Steed in the hand of the foreign agent Shelley who wants to torture him at the dental office.

Series 3:

Concerto: Steed burns his forearms as he tries to free himself.

The Nutshell: Steed has to go through a stressful Interrogation and shocks when he's suspected to be a traitor.

The Wringer: Steed suffers from confusion, hallucinations, and apathy before he gets rescued by Cathy Gale, and they have to crawl through ventilation shafts and a sewer to escape.

Series 6:

Killer: Steed against a killer machine.

Take-Over: Enemies try to kill Steed during hunting.

The New Avengers:

Dead Men are Dangerous: A former friend and old foe tries to kill Steed.

Positive Negative Man The Sell-Out The Surfeit of H2O Killer
The Grandeur That Was Rome They Keep Killing Steed The HourThat Never Was Castle De'Ath
Steed's ruffled curls in Take Over
Steed's Biography -
Ruffled and Tousled