Until modern humans arrived, every continent except Antarctica possessed a megafauna. In the Americas, alongside mastodons, mammoths, four-tusked and spiral-tusked elephants, there was a beaver the size of a black bear: eight feet from nose to tail. There were giant bison weighing two tonnes, which carried horns seven feet across.

The short-faced bear stood 13ft in its hind socks. One hypothesis maintains that its astonishing size and shocking armoury of teeth and claws are the hallmarks of a specialist scavenger: it specialised in driving giant lions and sabretooth cats off their prey. The Argentine roc (Argentavis magnificens) had a wingspan of 26ft. Sabretooth salmon nine feet long migrated up Pacific coast rivers.

During the previous interglacial period, Britain and Europe contained much of the megafauna we now associate with the tropics: forest elephants, rhinos, hippos, lions and hyenas. The elephants, rhinos and hippos were driven into southern Europe by the ice, then exterminated about 40,000 years ago when modern humans arrived. Lions and hyenas persisted: lions hunted reindeer across the frozen wastes of Britain until 11,000 years ago. The distribution of these animals has little to do with temperature: only where they co-evolved with humans and learned to fear them did they survive.

Most of the deciduous trees in Europe can resprout wherever the trunk is broken. They can survive the extreme punishment – hacking, splitting, trampling – inflicted when a hedge is laid. Understorey trees such as holly, box and yew have much tougher roots and branches than canopy trees, despite carrying less weight. Our trees, in other words, bear strong signs of adaptation to elephants. Blackthorn, which possesses very long spines, seems over-engineered to deter browsing by deer; but not, perhaps, rhinoceros.

All this has been forgotten, even by professional ecologists. Read any paper on elephants and trees in east Africa and it will tell you that many species have adapted to "hedge" in response to elephant attack. Yet, during a three-day literature search in the Bodleian library, all I could find on elephant adaptation in Europe was a throwaway sentence in one scientific paper. The elephant in the forest is the elephant in the room: the huge and obvious fact that everyone has overlooked.

Since then much of Europe, especially Britain, has lost most of its mesofauna as well: bison, moose, boar, wolf, bear, lynx, wolverine – even, in most parts, wildcat, beavers and capercaillie. These losses, paradoxically, have often been locked in by conservation policy.

Conservation sites must be maintained in what is called "favourable condition", which means the condition in which they were found when they were designated. More often than not this is a state of extreme depletion, the merest scraping of what was once a vibrant and dynamic ecosystem. The ecological disasters we call nature reserves are often kept in this depleted state through intense intervention: cutting and burning any trees that return; grazing by domestic animals at greater densities and for longer periods than would ever be found in nature. The conservation ethos is neatly summarised in the forester Ritchie Tassell's sarcastic question, "how did nature cope before we came along?"

Through rewilding – the mass restoration of ecosystems – I see an opportunity to reverse the destruction of the natural world. Researching my book Feral, I came across rewilding programmes in several parts of Europe, including some (such as Trees for Life in Scotland and the Wales Wild Land Foundation) in the UK, which are beginning to show how swiftly nature responds when we stop trying to control it. Rewilding, in my view, should involve reintroducing missing animals and plants, taking down the fences, blocking the drainage ditches, culling a few particularly invasive exotic species but otherwise standing back. It's about abandoning the biblical doctrine of dominion which has governed our relationship with the natural world.

The only thing preventing a faster rewilding in the EU is public money. Farming is sustained on infertile land (by and large, the uplands) through taxpayers' munificence. Without our help, almost all hill farming would cease immediately. I'm not calling for that, but I do think it's time the farm subsidy system stopped forcing farmers to destroy wildlife. At the moment, to claim their single farm payments, farmers must prevent "the encroachment of unwanted vegetation on agricultural land". They don't have to produce anything: they merely have to keep the land in "agricultural condition", which means bare.

I propose two changes to the subsidy regime. The first is to cap the amount of land for which farmers can claim money at 100 hectares (250 acres). It's outrageous that the biggest farmers harvest millions every year from much poorer taxpayers, by dint of possessing so much land. A cap would give small farmers an advantage over large. The second is to remove the agricultural condition rule.

The effect of these changes would be to ensure that hill farmers with a powerful attachment to the land and its culture, language and traditions would still farm (and continue to reduce their income by keeping loss-making sheep and cattle). Absentee ranchers who are in it only for the subsidies would find that they were better off taking the money and allowing the land to rewild.

Despite the best efforts of governments, farmers and conservationists, nature is already starting to return. One estimate suggests that two thirds of the previously forested parts of the US have reforested, as farming and logging have retreated, especially from the eastern half of the country.

Another proposes that by 2030 farmers on the European continent (though not in Britain, where no major shift is expected) will vacate around 75m acres, roughly the size of Poland. While the mesofauna is already beginning to spread back across Europe, land areas of this size could perhaps permit the reintroduction of some of our lost megafauna. Why should Europe not have a Serengeti or two?

Above all, rewilding offers a positive environmentalism. Environmentalists have long known what they are against; now we can explain what we are for. It introduces hope where hope seemed absent. It offers us a chance to replace our silent spring with a raucous summer. 

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