LONDON—The price of Brexit is starting to catch up to consumers here.

The June vote by Britain to leave the European Union triggered a steep drop in the British pound, putting foreign companies and importers—including electronics manufacturers, clothing retailers and car makers—in a bind: Do they raise prices in Britain to compensate for the falling value of sterling-denominated sales? Or do they hold tight, protecting market share at the expense of profit?

In recent days, many of them have decided on price increases. Others are warning higher prices are on the way.

U.S. and Asian electronics makers, whose component costs are typically in currencies like the dollar and yen, both of which have risen strongly against the pound, have been among the first to move. The pound is currently down more than 10% against the dollar since the June 23 vote.

Small shops along London’s Tottenham Court Road, long a marketplace in the city for electronics goods, said suppliers, including Dell Inc. and HTC Corp., have raised prices for many products by about 5% to 15% in recent days.

“Prices have definitely increased on all electronics,” said Sohel Amin, a manager at electronics outlet Itbex UK Ltd.

Texas-based Dell said in a recent statement the stronger dollar will have a direct impact on some of the products it sells to U.K customers. Sally Moore, a spokeswoman for the company, said the rate and timing of the increases vary across products, without offering details.

Taiwan-based HTC said last week it would boost the U.K. price of its new Vive virtual-reality headset by about 10%, from £689 ($918) to £759. It cited “recent currency valuation changes.” An HTC representative declined to comment more specifically on the pricing of other products.

Camera lenses and other components from Japan have been “especially up compared to before,” said Yalcian Sezen, manager at Sunrise Photographic Ltd.

On Thursday, Steve Dirnberger, a 30-year-old freelance videographer and travel blogger from South Africa, was shopping for gear for a wedding shoot in the U.K. and said he was surprised by the prices.

“It came to a lot more than we expected,” he said.

Apple Inc. iPhones and iPads aren’t yet going up. The company hasn’t adjusted prices to account for currency moves for any of the devices it sells here.

Germany’s Continental AG—the world’s second-largest automotive supplier by revenue—said Wednesday it had raised prices for its tires in the U.K., thanks to the big currency move. The company declined to say by how much. Car makers themselves haven’t yet disclosed any price increases, but executives in recent days have said it is only a matter of time.

“Everybody is now waiting for somebody to make the first step in terms of pricing adjustment,” said Carlos Tavares, the chief executive of Peugeot-maker Groupe PSA, during an earnings call last week.

British clothing and home-products retailer Next PLC warned customers Wednesday that a price increase was likely. Hennes & Mauritz AB last month said the uncertainly surrounding Brexit would affect U.K. sales but didn’t say whether it would raise prices.

There isn’t yet comprehensive price data across sectors in the six weeks since the Brexit vote. But economists have raised inflation forecasts more generally, based on the falling pound and expectations of sharp imported inflation.

In its inflation report released Thursday, the Bank of England projected annual, non-energy import price inflation to reach 6% in the first quarter of next year, up from 1.3% in the year-ago period. It cited the falling pound and said inflation would feed into higher consumer prices eventually.

Market-research firm Euromonitor raised its baseline inflation forecast for the U.K. after the Brexit vote. It has revised its forecast for next year up 0.7 percentage point, to 2.3%, and up 0.8 percentage point, to 2.7%, in 2018.

Big food retailers don’t appear to have raised prices, and may not for some time. Many have hedges that insulate them somewhat from higher import costs. Competition between British grocers has also made it hard to pass along price rises, but analysts expect higher food prices eventually.

“Historically one third of the movement in currency has fed through to food inflation, although shorter term hedging has normally resulted in a 5 to 9 month delay in the effect feeding through,” wrote Bernstein analyst Bruno Monteyne.

The currency moves have been a boon to British exporters and their customers overseas. Aydin Kurdash sells handmade shoes that average around £750 a pair through his London-based Gina Shoes Ltd., which exports to Europe and the Middle East. He expects to lower prices in those markets—perhaps by as much as $150 a pair—when the company rolls out its lineup for next season.

“Our costs have come down,” Mr. Kurdash said. “And our products have become more competitive as a result of the low pound.”