Currently, in Britain I am largely restricted in my freedom of movement, despite thousands of miles of footpaths, bridleways and other rights of access,. Furthermore, in England and Wales, I cannot camp in the 'wild' – instead I must pay to use a campsite.
Implementing Allemannsrett in Britain would change this: it allows everyone to use rural, uncultivated land for walking, camping, foraging and other outdoor activities, regardless of who owns it.
An objection might be that this infringes on the right to personal property, but I believe Allemannsrett is in accordance with J.S. Mill's harm principle. The laws of the Nordic countries clearly demand that those taking advantage of the Allemannsrett are respectful to the land they are using: there are rules concerning littering, the lighting of fires and so on. The saying 'take only pictures, leave only footprints' sums it up well. Therefore, those who use Allemannsrett properly are acting within the basic libertarian principle. The rules on foraging, and other more controversial aspects could be adapted as desired.
Another issue is that of privacy: landowners would not want hikers peering in through their windows. The Nordic laws cover this as well: any 'trespassers' must maintain a respectful distance from houses or cabins at all times (at least 150 metres in Norway).
A final objection is the claim that it would be pointless to introduce the Allemannsrett in Britain as it is in Scandinavia, since here we have a much higher population density. But the vast majority of the British population lives in urban areas, and the country has many places of natural beauty and sparse population where greater rights of access could allow much greater appreciation of them.
Allemannsrett in Britain would allow each individual to enjoy the countryside to its full extent. It would out us back in touch with our ancestors, by allowing us to camp 'wild', away from the mod-cons of everyday life. All this could be achieved without infringing on the basic principle of liberty, as clear rules would ensure respect for the land and its owner.