Here you have an international forum, so for British people at least this is a chance to learn from users who live in areas where big carnivores and other big animals still (or again) live in densely populated areas. There must be a hundred members who live not far from wild wolves, some users from the U.S., Canada and Scandinavia live next to bears, coyotes and cougars and so on.
In Britain, the problem is neither biological nor social. It is well known that large carnivorous birds and mammals can biologically thrive in Britain now, and the majority of people welcome it.
The problem is bureaucy or legal: how to prevent a small minority of naysayers from blocking the plan. Because there is very little cost of protesting, a small minority of people in Britain can block release of big animals with little or no rational argument. Simply because they can.
In other countries, this is commonly overcome by bribery, creating some broader plan which gives some funds to the local community together with wildlife protection, especially under the guise of developing tourism or green infrastructure. This is far from safe, because often local communities consume the money and still object the conservation. Another plan might be making use of land ownership peculiar to Britain. Find a large area of land where owners support wildlife. Release animals there, and hope that opponents elsewhere are more big mouth and little action and would not effectively kill the animals when they spread elsewhere.