Protecting medical supplies will be among the priorities for Fylde coast hospitals if the UK leaves the European Union on October 31.
But health chiefs have been warned by government not to stockpile and to prescribe medicines as usual for patients.
A meeting of the Blackpool Teaching Hospitals NHS Foundation Trust, held in public, heard a response programme was in place including the formation of the Trust's own task force.
A report to the board said Trusts had been told they "must not stockpile locally" and should avoid issuing longer prescriptions.
Vaccines must also not be stockpiled "beyond business as usual levels", while "organisations should reassure patients that arrangements are in place to ensure availability of vaccines post EU exit."
A national medicines shortage response group has been set up.
The report said: "Senior pharmacy leaders are expected to support local collaberation to meet patient needs."
But concerns were raised about the added burden a possible Brexit could put on hospitals as they enter the winter months when there is already additional pressure on medical services.
Berenice Groves, interim director of operations for the Trust, said there was still "a lot of confusion" about what may or may not happen with Brexit.
This needed to be handled in the coming months on top of the usual winter pressures and the possibility of "significent" weather disruptions.
She said the Trust's own task force was preparing for any possible outcome, and added: "They are ready to step up and there are clear actions in place nationally and regionally to set up our response."
Non-executive director Michael Hearty said: "Human nature is that people panic. This report is focused on supply, but what about demand?
"People will feel that for whatever reason they will want extra help."