An open letter from public leaders in Cumbria is urging people to "stay safe and stay local" during lockdown.
Signed by authorities and MPs, it states: "Whilst it may be tempting to go out for a scenic drive in the Lake District, now is the time to stay home."
Mountain rescue teams have also made a plea for people to "exercise locally".
It comes as several hospitals suspended outpatient appointments to cope with a rise in a coronavirus cases.
On Friday 1,325 deaths within 28 days of a positive Covid test were recorded in the UK - the highest daily figure yet - along with 68,053 new cases.
The letter states everyone needs to "play their part" to make sure that Cumbria is ready for the return of visitors "when it is safe to do so".
"All authorities and partners in Cumbria are appealing to residents and visitors to adhere to the new lockdown guidance.
"We're fortunate in living in Cumbria in that we are surrounded by many outdoor spaces on our doorstep, so why not explore the beautiful parks and walks close by and while you're out support your local shop by shopping local."
Lake District Search and Mountain Rescue Association chairman, Richard Warren, said: "Cumbria's Mountain Rescue teams are appealing to visitors to think carefully about their plans for outdoor activities.
"We are asking all hill-goers to be considerate of the resources of the emergency services at this time.
"We can all help by staying at home, only exercising locally to our villages, towns and cities, avoiding risky activities and high mountain terrain, sticking to lowland paths and walkways while strictly observing social distancing principles and the new government lockdown rules."