Hamilton is bidding to win his seventh race at a spectator-less Silverstone, but after trailing Verstappen in the early running, he was three tenths down on Stroll later in the day.
Alexander Albon finished second, but his afternoon ended in the barriers after he lost control of his Red Bull through the right-handed Stowe corner.
Albon, just 0.080 seconds slower than Stroll before his accident, suffered damage to both the left-rear and left-front of his car following the high-speed smash.
The London-born Thai walked away unscathed from the incident, but his Red Bull crew will work long into the evening to ensure his machine is ready for qualifying on Saturday.
Valtteri Bottas, who trails Mercedes team-mate Hamilton by five points, finished third ahead of Ferrari's Charles Leclerc. Verstappen was fastest in the morning running before finishing a distant 14th in the concluding action of the day.
A car failure prevented Sebastian Vettel from completing any running on Friday morning, and, despite returning to the track for the second session, the four-time world champion could manage only 18th of the 20 runners, 1.58 seconds off the front.
Hamilton started the weekend as the favourite to win on Sunday, but on the basis of Friday's evidence, the Briton will not have it all his own way as he chases a third win in four races this term.
Traditionally, the Mercedes cars have struggled in high temperatures and with the mercury hitting the mid-thirties here on a sweltering day, there was little for the all-conquering team to shout about.
"It was quite a difficult day," said Hamilton. "The wind made it really tricky with the car and the balance is not as good as I would have liked so we are going to work on it and figure it out.
"Hopefully we will make some good changes overnight. It is not a disaster but it has definitely been a hard-day driving."
Racing Point have modelled their machines on last season's championship-winning Mercedes, and in the absence of team leader Sergio Perez following his positive coronavirus test, Stroll took on the baton for the Silverstone-based team.
The Canadian finished top, with Nico Hulkenberg, deputising for Perez, seventh in the running, six tenths behind his team-mate.
Hulkenberg has been out of action since he was dropped by Renault last year, but the German, a veteran of 177 grands prix starts, could be back in action again here next weekend if Perez is forced to remain in quarantine.
Elsewhere, British driver Lando Norris finished 11th, five spots behind Carlos Sainz in the sister McLaren. George Russell was 17th for Williams.
