Britain reported 1,000 new cases of coronavirus on Sunday, the highest number of new cases recorded since late June.
England accounted for 988 of the newly reported cases. Britain has the highest death toll in Europe with more than 41,000 deaths.
Throughout Europe, officials have been warning of a resurgence in virus cases, particularly among young people, who have more social contacts and have relaxed their social distancing.
Officials in Europe have also warned that people travelling on holiday could be a risk.
"We're in the midst of a global pandemic and that means there is always the risk to travel plans," British finance minister Rishi Sunak told Sky News.
Sunak said that the British government kept travel restrictions constantly under review.
Several European countries have reported a rise in new daily cases.
France reported more than 2,000 new cases of coronavirus and said that 184 clusters are currently under investigation. For weeks after lockdown, the country had been reporting a few hundred daily cases.
Italy, which has kept case numbers low since exiting lockdown, also said there was a rise in cases.
Spain had a 14-day average of 89.4 cases of coronavirus per 100,000 people, according to the European Centre for Disease Control (ECDC). Luxembourg was the only country with a higher rate of cases per 100,000 people than Spain.
Many cities in Europe have now issued stricter guidelines on wearing masks in public spaces in an effort to curb infections.