It seems like it would be a combination of loss of the way it has been and of the beneficial effects of grazing.
Grazing can have both positive and negative effects, and can benefit certain species at the expense of others so its all a balancing effect.
Cattle are thought to provide biodiversity benefits in woodlands when grazed at low density since they eat dense vegetation of a low digestibility and break up vegetation mats with their hooves. This opens up the ground layer vegetation and is thought to be beneficial for tree regeneration as well as leading to a greater variety of vegetation types and associated invertebrate and bird assemblages. Because of these perceived benefits there is increasing interest in the use of cattle as a tool for nature conservation management in woodlands.
Impacts of large herbivores on woodlands - Survey of cattle grazed woodlands in Britain
Over the last century human activities have
moved away from using woods for their food and
livelihoods. The loss of woodland management
allowed many sites to become neglected, overgrown
and shady. This led to a serious decline in many
species that require disturbance and more open
conditions, including rare lichens and ground flora.
Wood Wise – Woodland Conservation News Autumn 2012
Dunwich Forest ponies Steve Aylward
Overstocking of woodland grazers can cause
a loss of plant and animals species and prevent
natural regeneration, through soil compaction and
overgrazing. But balanced regimes with appropriate
grazing pressure can increase habitat diversity,
support important wildlife populations and
encourage natural regeneration. A lack of grazing
often allows more aggressive plants to outcompete
and dominate sites.
Woodland grazing – introduction
Several papers report examples of successful use of livestock in forest management in terms of controlling woody understorey vegetation, with benefits to tree growth and in some cases, ground flora. In Britain, stock could potentially play a similar role in helping to eliminate competing vegetation.
The literature is unanimous in that for grazing to be successful it must be applied at a suitable livestock density, and duration of grazing and grazing season be appropriate to the situation.
Individual study: A literature review of the effects of sheep and cattle grazing in plantation forests
The disappearance of grazing from much of British lowland heathland over the last century is thought to be a major contributory factor in the loss of health vegetation by allowing succession towards woodland. The reintroduction of grazing is hindered by the small amount of available information on grazing management methods or on the responses of lowland heath vegetation to grazing.
Grazing of lowland heath in England: Management methods and their effects on healthland vegetation
Its also worth pointing out that most of these mention that there isn't a lot of study on these the effects of grazing.