Defra minister George Eustice, who like Leadsom supported Brexit, said: "We have a unique opportunity to unbundle the confusing and conflicting parts of the CAP (EU Common Agricultural Policy) and to look at other approaches in countries like Canada and Australia. We can think things through from first principles."
He added: "We want to move away from subsidies, which increase the cost of rents and farm inputs and undervalue food, and to support farmers in better ways to become vibrant, profitable and able to deliver ecosystem services. You have a role to play in enhancing the environment and we will pay you for it."
Northern Ireland farming minister Michelle McIlveen, also a Brexit supporter, said: "Northern Ireland is a net food exporter so this is much more important than for the rest of the UK, and it will be the only UK region with an EU land border. It's an opportunity for change including removing bureaucracy."
Describing herself as "a passionate remainer", Welsh cabinet secretary for rural affairs Lesley Griffiths said: "I don't see a 'UK agriculture policy' any more but we will need UK frameworks in place based on agreements with all four administrations. I don't see a time when we won't have payments for farmers."
Calum Kerr MP, the SNP's rural affairs spokesperson in Westminster, said: "Repatriation of powers shouldn't mean centralisation of control in London rather than Brussels. Support payments are critical to farmers in Scotland. They represent two-thirds of total farm income. It should be a core principle that we retain farm profitability."
Eustice responded: "Area-based payments don't work very well. I am more interested in risk management and support for increased productivity and profitability, targeting active rather than 'slipper' farmers," adding: "We don't want distortions in the UK market" through different administrations pursuing separate policies.