Scotland and Wales reopened restaurants, cafes, and nonessential shops on Monday, marking the next phase of a gradual relaxation of coronavirus restrictions that have been in place for months.

In Scotland, restaurants can serve food but not alcohol indoors until 8 p.m., and they can serve food and alcohol outdoors without restrictions. Stores, beauty salons, museums and galleries also reopened, and people are permitted to book travel in the rest of Britain.

The first minister of Scotland, Nicola Sturgeon, said she was hopeful that the country would continue its progress and lift more restrictions by the summer. But she cautioned that the virus was more infectious now than it had been in earlier waves and, therefore, “We must stick to the rules.” Free rapid tests will be available to the public.

In Wales, places of worship and retail stores reopened, and restaurants resumed outdoor service. Outdoor wedding receptions with up to 30 people can take place.

Cases remain low in Britain, with more than 40 percent of the population having received at least one dose of a vaccine. On Sunday, the country reported just over 1,700 new cases and 11 deaths, according to a New York Times database.