Blackpool Council says it is "ramping up" its preparations should the UK leave the EU on October 31 under a no-deal arrangement.
The council has received specific government funding of £315,000 to address the planning and possible consequences of Brexit.
Director of Resources Steve Thompson is leading a dedicated task force which meets weekly and is in direct contact with channels including the Home Office, regional officials and the Department for Exiting the EU.
Issues being addressed include the registration of EU nationals for the EU settlement scheme while the management of supplies of food, medicines and fuel are also being prioritised.
There is also liaison with local businesses on matters such as export health certificates and other regulatory activities.
A report to full council says: "The council is ramping up its business continuity planning should the UK leave the European Union on October 31 under a no-deal arrangement."
A meeting of the council's Audit Committee in July heard the main concerns which could disrupt council services were the breakdown of supplies of fuel and medicine.
But chief executive Neil Jack said the authority would ensure the resort's most vulnerable residents were protected.
This included ensuring there was enough fuel to keep key staff such as social workers on the road.
Mr Jack told the Audit Committee: "Most of the risk we cannot manage. If fuel doesn't arrive in the UK, we can't manage that.
"But we can understand the implications and how we prioritise where those resources go. It's about being ready to mitigate the consequences.
"We can't manage the supply of fuel to Blackpool but we can make sure vulnerable people are prioritised."
A recent meeting of the Blackpool Teaching Hospitals NHS Foundation Trust, held in public, was also told it has a response programme in place including 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 collaboration 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 extra pressure on medical services.