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Housing and Communities Secretary James Brokenshire says there has to be a "seamless border" in Ireland.
Political reporter, BBC Sussex
The Government will give local councils £56.5m over two years to help them plan for Brexit.
Counties like Kent, West Sussex or Surrey would be given £185,000 each for 2018/19 and 2019/20.
Districts and Boroughs like Hastings or Chichester would get £35,000, while unitary authorities like Medway or Brighton will be given £210,000.
In addition, the Government has set aside £1.5m to help councils with planning around ports on their patch, and another £10m to deal with issues that emerge after the UK has left the EU.
The Communities Secretary, James Brokenshire, told MPs the funding would "help councils to adapt to changes caused by Brexit, while still protecting vital local services".
He added that other Government departments may make further funds available to local authorities.
But some councillors have raised concerns the cash might not cover all of their Brexit-related costs.
It comes as the council in Brighton and Hove revealed it was looking at 825 separate ways that the UK's departure from the EU might affect the city.