Hill produced a lap of 1:26.767 right at the end of the session to jump up from sixth position to first.
Shane 'Shakey' Byrne (Rapid Solicitors Kawasaki) finished in second place in the session with Graeme Gowland (WFR Honda) third.
MCE Insurance British Superbike Championship, Brands Hatch, free practice one:
Tommy Hill (Swan Yamaha) 1m:26.767s
Shane Byrne (Rapid Solicitors Kawasaki) +0.031s
Graeme Gowland (WFR Honda) +0.89s
Alastair Seeley (Tyco Suzuki) +0.171s
Alex Lowes (WFR Honda) +0.312s
Josh Brookes (Tyco Suzuki) +0.388s
Noriyuki Haga (Swan Yamaha)
Chris Walker (Pr1mo Bournemouth Kawasaki)
James Westmoreland (WFR Honda)
Michael Laverty (Samsung Honda)