Kim, 45, wore grey hooded top with matching flared jeans and a pair of heels.

The Skims founder had her brunette locks down and opted for a chic make-up look, complete with mascara and a nude lip.

Meanwhile, Lewis sported a cream jumper with baggy denim jeans and a pair of red boots.

The F1 star attempted to go incognito with some black sunglasses and a baseball camp.

The two were seen heading back into a vehicle as they made their way home after the shopping trip.

Just last week, Kim made an 11,000-mile round-trip to spend 24 hours in London with Lewis, 41.

She flew to the UK on her private jet to see her man in a bid to keep their long-distance romance alive.

She left Los Angeles on Monday night and landed at Farnborough, Hants, at 4pm on Tuesday before being chauffeured on a 90-minute journey to Lewis’s £18million home in Kensington, West London.

The couple stayed holed-up in his six-bedroom mansion while their security teams kept guard.

She then left on Wednesday afternoon, taking off from Oxford at 5.30pm to return to the US.

A source said: “Lewis and Kim are two of the busiest people in showbiz, but they are determined to do everything to see each other when they have any spare time.

“Kim spent Easter weekend with her family and then had a photoshoot in Los Angeles on Monday morning, then flew across the Atlantic to see Lewis.

“They didn’t have long together because she had commitments in the US to get back to, but it was quality time.”

Kim’s romance with Lewis became public knowledge after The Sun revealed she flew in from Los Angeles on her £100million private jet to spend an evening with him.

On January 31, the couple enjoyed a brief stay at the exclusive Estelle Manor in the Cotswolds, with insiders saying they had the spa to themselves, before enjoying a meal in a private room.

They made their public debut as a couple at the Super Bowl in February where they were spotted sitting together in a luxury suite.

Proving they’re the real deal, the sports star recently met Kim’s children while they were out in Tokyo ahead of the Japanese Grand Prix.

The couple were  joined by three of her children -Saint, 10, Chicago, nine, and six-year-old Psalm – while they were on spring break.

“It’s more than just a casual connection. It takes a lot to capture Kim’s interest and she’s definitely intrigued,” an insider told People.

“He’s just an easygoing guy with great energy.

“Her family likes him and Kim’s very into him. They are both busy with their careers, but see each other as much as possible.”

They were also joined by her sister Khloe, 41, and her children, True, seven, and Tatum, three.