The Dutchman stretched his lead over Hamilton by winning the sprint and takes a 33-point advantage over the beloved local driver in Sunday's grand prix.
"In my opinion there needs to be a Saturday and Sunday weekend," Hamilton said.
Verstappen and third-place Valtteri Bottas said they preferred the the traditional three-round qualifying, noting they'd rather have used the track time for practice.
The leaders of F1 have recognized the series needs a freshening as its audience starts reaching key younger demographics and so this weekend they tried something new. One practice session was cut and transitioned instead Friday to the preferred knockout qualifying, which was won by Hamilton.
But that only set the starting grid for Saturday's sprint race — dicey because there's always the chance the drivers don't push hard out of fear of damaging their cars a day early when points aren't on the line.
That wasn't a problem because it was racy right from Verstappen's jump on Hamilton as flames shot from Verstappen's heated left front tire. Fernando Alonso jumped from 11th to fifth in the opening lap before finishing seventh, and Sergio Perez Jr. crashed.
Any chance at Hamilton finally bettering the championship leader was lost when Verstappen simply drove away from Hamilton at the start.
"They've done a really great job with their engine, their starts are really great this year," Hamilton said. "We've lost a bit of performance on our starts, so we've got to work a bit harder to improve that."
Verstappen earned three points for the win, as well as the pole for Sunday's full Grand Prix. It put Verstappen in position for a fourth consecutive win, all from pole.
Red Bull has won five straight, which includes a Perez victory. He was the biggest casualty of the experimental qualifying when Perez crashed on the fifth lap and finished last.
The hard racing was celebrated after the finish as Verstappen, Hamilton and Bottas instead of going to a podium, climbed aboard the trolley. Verstappen was presented with an old-school winner's wreath around his neck and all three drivers waved to fans as they passed.
For the fans, Hamilton was jovial yet apologetic for the defeat.
"I've got to give a lot of love to all these fans, I can't tell you the energy that I'm getting from them is awesome," Hamilton said. "I am sorry I was not able to get the win; tomorrow we fight again."
Verstappen was content with the win.
"Happy to have pushed for those three points," he said. "A good fight with Lewis on the first lap,"
Hamilton received two points for finishing second. Bottas earned the final point awarded Saturday.
Hamilton has not won a race since May 9 at the Spanish GP but Silverstone has long been a Mercedes stronghold and the team has won seven of the past eight British GP. Hamilton has won six of those.