Climate change activists representing Just Stop Oil invaded the track at Silverstone on Sunday during the first lap - simultaneously a red flag due to Guanyu Zhou’s crash brought an electric start to a halt.
Seven protestors were arrested, Northamptonshire Police confirmed.
“If it’s not already too late, history will look back very favourably on these people,” said former England footballer and BBC pundit Lineker.
Sky F1 expert and former driver Brundle replied: “Gary please don’t encourage this reckless behaviour.
“They’d have been sliced into 100 pieces and fans, marshals and drivers were wholly at risk of injury and death.
“We already had one lucky escape.
“I totally 100% support freedom of speech and opinion, but do it responsibly.”
Lineker hit back: “Way more risk of death with climate change to everyone than there is attempting to delay a motor race.”
Hamilton initially said “big up those guys” when told about the protestors.
“I love that people are fighting for the planet,” he said. “So we need more people like them.”
Mercedes said: “Lewis was endorsing their right to protest but not the method that they chose, which compromised their safety and that of others.”
Hamilton later posted a message on his Instagram story which read: "As we've seen today, this is very dangerous sport. I wasn't aware of the protests today, and while I'll always support those standing up for what they believe in, it must be done safely.
"Please don't jump on to our race circuits to protest, we don't want to put you in harms way."