An overwhelming majority of the British public polled want new post-Brexit laws protecting wildlife and the countryside to be at least as strong as the EU rules currently in place, according to a opinion poll published on Thursday.

Many also want a new farming subsidy regime to emphasise environmental protection more than the EU’s existing Common Agricultural Policy and the vast majority want an EU ban on neonicotinoid pesticides, known to harm bees and other pollinators, to remain in place.

Much of the protection of British wildlife and the environment stems from EU’s birds and habitat directives, but these will have to be replaced when the UK leaves the bloc. Farming minister George Eustice campaigned for the UK to leave the EU and told the Guardian in May that these directives were “spirit crushing” and “would go”.

But the national poll, conducted by YouGov for Friends of the Earth, found that support for the same or better environmental protection was high even among those who voted to leave the EU.

Overall, 83% of people said Britain should pass new laws providing better (46%) or the same (37%) protection for wild areas and wildlife as current EU laws, with only 4% wanting lower protection. Of those who voted to leave, 46% wanted better protection, 39% the same and 6% less protection.

The poll found 88% of people wanted the neonicotinoid ban to stay in place after the UK leaves the EU, with just 5% wanting the ban to be scrapped. The National Farmers Union (NFU) opposes the ban, arguing that it blocks useful protection of oil seed rape crops, but the ministers recently rejected an NFU application for an “emergency” lifting of the ban.

EU farming subsidies are currently worth £3bn a year to UK farmers and include some schemes for improving the environment. The poll showed 57% of the public want more emphasis (25%) or the same emphasis (32%) on environmental protection. Only 7% of people wanted less emphasis on environmental protection, while 11% said there should be no subsidies at all.

Chancellor Philip Hammond said earlier in August that existing levels of farm subsidies will be guaranteed until 2020, when there will be a “transition to new domestic arrangements”. The National Trust, a major landowner, recently called for complete reform of the British farm subsidy system after Brexit, ending payments for simply owning land and only rewarding farmers who improve the environment and help wildlife. The NFU criticised the plan, saying food production is vital.

Samuel Lowe, at Friends of the Earth, said: “This [poll] sends a powerful message to the UK government that EU rules aimed at protecting our natural environment must be maintained or strengthened. The poll completely undermines those who argue that Brexit should lead to a watering down of the UK’s environmental commitments.”

He said: “The government must also stand up to pressure from the NFU and keep the EU ban on bee-harming neonicotinoid pesticides. This is what the science says, and the public demands.”