He was just 0.033 seconds quicker than Rosberg as the dust settles on the controversy following their collision at Sunday's Austrian Grand Prix.
Mercedes say the drivers are on their "last warning" and risk "financial and sporting penalties" if they crash together again.
Hamilton is 11 points behind Rosberg in the championship going into the race.
Force India's Nico Hulkenberg was third fastest, 0.8secs behind the Mercedes and just 0.009secs ahead of Ferrari's Sebastian Vettel.
Even at this early stage, the margin between Mercedes and the rest suggests they will be in a world of their own this weekend, a continuation of the recent trend that has seen any sense of a threat from Ferrari evaporate.
And Vettel - who tested the new 'halo' cockpit safety system during the session - coasted into the pits at the end with what appeared to be a gearbox problem.
Red Bull's Daniel Ricciardo was fifth fastest, despite a wobble through Vale corner at the end of his lap, and ahead of Ferrari's Kimi Raikkonen, who it was announced before practice will stay with the Italian team for another season in 2017.
Red Bull's Max Verstappen was seventh, ahead of the second Force India of Sergio Perez, Toro Rosso's Carlos Sainz and the McLaren of Fernando Alonso, whose team-mate Jenson Button was 12th, behind the other Toro Rosso of Daniil Kvyat.
Alonso said before the weekend that McLaren were hoping for a step forward at Silverstone thanks to the circuit suiting their car better than recent races and a step forward in engine performance thanks to an intake/induction upgrade from Honda.
Englishman Jolyon Palmer was 17th fastest at his first British Grand Prix, 0.8secs ahead of reserve driver Esteban Ocon, who was driving Kevin Magnussen's car in the first session.
British Grand Prix first final practice results
British Grand Prix coverage details
Lewis Hamilton beat team-mate Nico Rosberg to the fastest time as Mercedes dominated British GP first practice.