Two sons of famous motorsport fathers breathed sighs of relief on Monday after ending long waits for success in an action-packed British Grand Prix.

Ferrari's Carlos Sainz, son of two-time world rally champion Carlos Sainz Sr, claimed his maiden Formula One victory in his 150th race, while Mick Schumacher, son of seven-time F1 champion Michael, finished eighth for Haas to score his first points.

"I think a first win is always a bit of a relief, I'm not going to lie," said Spaniard Sainz. 

"The same way that the pole position didn't feel like it, this win does feel a bit of a relief, because there you have it, you have a win in F1.

"And for sure, I'm going to keep fighting for more! I'm going to keep improving myself with this car and I'm going to try and make it happen."

Sainz had been cast as a reluctant second driver at Ferrari this season as Charles Leclerc made a winning start to lead the title race, but as the Monegasque's fortunes declined in recent months he rose to the challenge, overcoming a spate of accidents.

"I never stopped believing that this win was going to come," he said. "Even if this year has been tough for me -- and it hasn't been the easiest. In Monaco, I could have won.

"In Canada, it was super close and so it was about time that something just happened in a race that you can win. So, I keep believing.

"If there's one thing this sport has taught me, that's it. Things have never come easy in my career but this is a great example that it still happens."

Sainz's luck changed when, running second in the final stages of Sunday's race, he took advantage of a safety car deployment to take fresh soft tyres while Ferrari left Leclerc out on worn hards.

He had extra grip, passed his team-mate easily and drew clear to triumph.

Schumacher gives Verstappen scare 

As he did, several major scraps took place behind him –- in one of which Schumacher, 23, battled Max Verstappen, who had mechanical problems, for seventh before settling for eighth and four points.

"For me, it is a relief to get the media attention away from me at last and feel free to concentrate on my racing and my driving again," said the German who was given a thumbs-up from Verstappen at the finish.

As this unfolded, Schumacher's friend and mentor Sebastian Vettel was watching closely from his Aston Martin in ninth place.

"I was actually screaming inside the car like 'Go Mick -– go get him,'" said Vettel. "I'm very happy for him –- I think it's been a long time that he deserves the result and it's great to get it."

Schumacher had gone 29 races without a point and was under pressure from his team boss Guenther Steiner. His Haas team-mate Kevin Magnussen has scored 16 points this year, but on Sunday was beaten into 10th behind Vettel.

"Finally!" Schumacher shouted out on team radio as he finished. "I told you guys this is the week for me. Prove them wrong and believe in yourself -– that's what I say."

At the back of the Haas garage, his mother Corinna watched on, recalling perhaps that Mick was only five when Michael won his seventh title in 2004. He continued racing, but suffered a serious brain injury after retiring when skiing with Mick in December 2013.