Vaughan played his first county championship match of the season, against Hampshire, at Headingley on Wednesday, where he managed just one before being caught behind.
Cook, who made his name internationally with a hundred as an opener on Test debut against India in Nagpur in March, has been batting in Vaughan's number three position during the ongoing series with Sri Lanka despite the Essex left-hander having spent most of his career at the top of the order.
An innings of 89 in the drawn series opener at Lord's and a composed, unbeaten 34, which saw England home to a six-wicket win in the second Test at Edgbaston and a 1-0 series lead, suggested Cook was relishing his new role.
"At the moment I'm just happy playing for England and if that means batting at three, I've really enjoyed it," Cook told reporters at Trent Bridge, venue for the third and final Test against Sri Lanka, here Wednesday.
Cook has dropped to three after the restoration of the Andrew Strauss and Marcus Trescothick opening partnership and he admitted: "It's been a bit different watching Straussy and Tres go out and you are still sitting there, it took a little bit of getting used to."
Meanwhile, the 21-year-old Cook was phlegmatic about the prospect of Vaughan's return to the Test side for the four-match series with Pakistan, which starts at Lord's in July.
"It's great that he's back, it's good that his fitness is on the mend. It adds more strength to the England team, the England squad and we've always been slightly criticised for a lack of strength," he explained ahead of Friday's start to the Sri Lanka series finale.
"Everyone knows he's the captain and when he's ready fit and well he'll be back but it's up to all us now that no one is complacent and we keep scoring runs. If you are in the shirt and you're scoring runs then that makes selection very tough.
"For me personally, if I keep scoring runs and big runs I should hopefully keep my place."
"I'm not really worried about what happens in the future I'm just looking forward to the next time I play for England, trying to enjoy it and clinch this series against Sri Lanka."
One encouraging aspect of Cook's performance has been the way he has coped with Sri Lanka's master off-spinner Muttiah Muralitharan, who took 10 for 115 at Edgbaston.
"I've seen a little bit more of him but he's a genius and he's still tough to face. All his variations make it hard. But the more you look at him, the more you play against him, the more clues you pick up," Cook said.
"At Edgbaston, it was nice to get my first win for England, good to go 1-0 up in the series and I was glad I was out there getting a red-inker at the end, seeing us home.
"You see his (Murali's) smiles, you see his eyes. He's just a competitor and wants to get you out every ball. He's a great bowler and I've enjoyed facing him."
Cook said the particular problem with Murali was the lack of difference in his action for his stock off-spinner and the 'doosra', the ball that turns the other way.
"The first thing is trying to pick any clues in his action. There is a little bit of a difference but it's so marginal.
"I just try to see that and watch the ball spinning. Sometimes you get it, sometimes you don't because he (Murali) scrambles the seam and it's just good luck from there.
"When you are watching him you are doubly focused about which way it is going to turn.
"He does mix it up as well. They (the deliveries) are so similar it's tough. On not real helpful wickets, it shows what a threat he is."