The Peak District National Park Authority says it has received reports of unauthorised closures of footpaths and legal rights of way.
It said unofficial signs had been erected by footpaths with some being closed-off or blocked for access in Buxton and Hayfield, Derbyshire.
It said some Peak District residents had been prevented from being able to exercise locally, while those who are key workers have reported their route to work being inaccessible and their cars being targeted with signs about staying at home.
Sarah Fowler, chief executive of the authority, said: "I can understand a reaction to the high numbers of visitors we saw last week could, for some, be seen as needing to set up makeshift closures and blockages to rights of way.
"However, this is unauthorised activity... there have been no changes to rights of way legislation as a result of the Covid-19 measures."
The authority said any signs referencing the Peak District being closed were not in line in their official signage and thanked people who had listened to advice and stayed at home, or exercised closer to home.
A couple who were forced to cancel their wedding amid the coronavirus pandemic are donating their wedding favours to “lift the spirits” of NHS staff.
Friends and family had been set to fly in from around the world to celebrate Shevaun and Steven’s big day on Saturday
The couple, from Purley, had planned to tie the knot in the Peak District – where they enjoyed their first holiday together but after weeks of uncertainty about whether it could go ahead, the venue offered them a postponement last week.
Shevaun, 38, said they had now chosen to give the 100 luxury biscuits intended for wedding guests to front-line health workers instead.
“We wanted to share our appreciation to all the staff at the Croydon University Hospital for all their hard work in these scary and troublesome times,” she said.
Like many other couples with weddings booked at this uncertain time, they have decided to postpone it until 2021.
Shevaun, an executive assistant, said: “When the crisis started we thought we might have to go ahead with the wedding with just us two and a couple of friends. My family from different countries couldn’t fly over.
“It got to the point where we thought, ‘we’re not going to have fun here, it is not actually going to be that enjoyable’. We didn’t really want to start our married life that way.”
Despite the turn of events, the bride-to-be remains upbeat.
“It wouldn’t have been much fun in the current crisis,” Shevaun said. “‘You may now elbow bump the bride’ lacks a certain romance, wouldn’t you say?”