Swatch announced it was closing a store in Greater Manchester on Sunday for a second day after scores of people queued for the launch of a new pocket watch.
Police were called to the Swatch store at the Trafford Centre in Greater Manchester on Saturday, with an arrest also made in Cardiff.
Videos posted online appeared to show huge crowds at multiple shopping centres across the UK with police near a number of stores.
Police were called to a shopping centre in Cardiff after reports of about 300 people trying to get in to a Swatch store at 6.20am on Saturday, South Wales Police said.
A 25-year-old man from Pengam was arrested and issued with a Section 35 dispersal notice, the force added.
Officers were also sent to the Trafford Centre in Manchester and "dispersed a large number of people," Greater Manchester Police said.
Swatch posted on Facebook on Saturday saying "in light of safety considerations for both our customers and our staff" stores in Liverpool, Manchester, Birmingham, Sheffield, Glasgow and Cardiff would be closed for the day, along with all of the London stores.
It posted later on Saturday saying: "To all our dear fans worldwide of our AP x Swatch collab, launched on May 16.
"To ensure the safety of both our customers and our staff in Swatch stores, we kindly ask you not to rush to our stores in large numbers to acquire this product.
"The Royal Pop Collection will remain available for several months. In some countries, queues of more than 50 people cannot be accepted, and sales may need to be paused."
The company posted again on Sunday saying the Manchester store would be closed for the day "in light of safety considerations".
Swatch launched the Audemars Piguet x Swatch Royal Pop Collection on Saturday at selected stores worldwide, according to the company's website.
Purchases are limited to one watch per person, per day and per store.
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