There were 160,000 fans at Silverstone for the race on Sunday
McLaren's Lando Norris fought off an attack from Lewis Hamilton's Mercedes after a late safety car to finish second and give the 160,000 fans a double home podium to cheer.
Verstappen's eighth win in 10 races this year brought Red Bull level with the record McLaren established in their historic 1988 season with Ayrton Senna and Alain Prost.
Oscar Piastri made it a great day for McLaren with fourth, ahead of George Russell's Mercedes.
Verstappen was untouchable out front, once he had overtaken Norris for the lead on lap five after the McLaren jumped ahead when the world champion suffered too much wheelspin at the start.
This victory, which puts Verstappen's championship lead over team-mate Sergio Perez at 99 points, extends a run of Red Bull wins that dates back to last season's Abu Dhabi Grand Prix.
On Verstappen's current apparently unbeatable form, Red Bull will break McLaren's record at the next race in Hungary in two weeks' time and are likely to move far beyond it as the season progresses.
Verstappen reduced this grand prix, like so many this year, to a demonstration run once into the lead.
But behind him the race, static for a long period, came alive after the safety car, which was called when Kevin Magnussen's Haas caught fire down the Wellington straight.
Divergent tyre choices introduced jeopardy and intrigue for everyone else over the final 14 laps.
Norris and Piastri had looked on course for a double podium for McLaren, who introduced a major upgrade for Norris to great effect at the last race in Austria and gave it to Piastri at Silverstone as well.
But the safety car changed everything and gave Hamilton a chance not only to jump ahead of Piastri but also to briefly threaten Norris.
The seven-time champion, who started seventh, drove steadily in the opening laps, biding his time once he had re-passed Fernando Alonso's Aston Martin, which overtook him on the first lap.
Hamilton moved up as the pit stops started to happen ahead of him, with first Charles Leclerc pitting his Ferrari out of fourth place, followed by the second Ferrari of Carlos Sainz, the Mercedes of Russell, and Piastri.
It meant Hamilton was on course to finish fifth behind Piastri and Russell, but stopping under the safety car allowed him to jump both and line up behind Norris at the restart.
Norris had hinted heavily several times before his stop that he might prefer the soft tyre, without ever explicitly asking for it, and McLaren stuck with their choice for hards as he came in, just as a virtual safety car turned into a full safety car, because changing tack would have caused too many risks and created too big a delay.
Norris expressed over the radio his fears that he would struggle to hold Hamilton back, with the Mercedes on soft tyres and the McLaren on hard, but the 23-year-old weathered an early storm after the restart with aplomb and then edged away to consolidate his second place.
Piastri, also fitted with hard tyres at his pit stop, was equally impressive in a car not quite up to the same specification as his team-mate, lacking a new front wing.
The Australian rookie lost his hopes of a podium with the safety car, which allowed Hamilton to jump him.
But in the closing laps, as Hamilton dropped away from Norris, the Mercedes came under pressure from Piastri, who crossed the line less than a second behind.
Russell was the only man in the top 10 to choose soft tyres rather than mediums for the start, and he jumped up a place to threaten Leclerc for fourth place.
But he lost out by stopping before the safety car and came home fifth as Sergio Perez recovered from yet another poor qualifying session to finish sixth from 15th on the grid.
The last driver he passed was Alonso, whose Aston Martin team have in the last few races fallen away from their strong form in the first six races of the season.
Ferrari's day crumbled after a promising start. Leclerc had no pace in the first part of the race, spending the first half of the race with Russell right behind him not quite managing to get past.
Leclerc made an early stop for hard tyres and then came in again under the safety car for mediums.
But he again struggled and lost eighth place to the impressive Williams of Alex Albon, who chose soft tyres at the safety car, in the closing laps.
Sainz, who was left on hard tyres when he did not stop under the safety car, lost three places in a few corners as Perez, Leclerc and Albon all passed him after the restart, and trailed in a disappointing 10th.
-- Courtesy of BBC Sport