Doctors and pharmacists are being told not to give patients extra prescriptions in advance after Brexit.
The NHS has stockpiled medication in case of difficulties in the event the UK leaves the EU without a deal at the end of this month.
There have been concerns that it may be problematic to get some supplies into the country because of a potential backlog at ports.
But Wakefield Clinical Commissioning Group (CCG) says that patients do not need to panic or obtain extra medicines for their own kitchen cupboards.
Health bosses want to avoid a situation where people end up with more prescripted drugs than they actually need.
Speaking at a board meeting on Tuesday, the CCG's director of corporate affairs, Ruth Unwin, said that steps had been taken by the NHS to ensure the system continues to run smoothly.
And she suggested that problems may only occur if the public "don't believe" that the situation is in hand.
She said: "The preparation work we’ve been doing applies whether there’s a deal or no deal really.
"There are no unmitigated risks we’ve identified at this time, which means there isn’t anything happening that we don’t know about.
"We’ve had assurances from NHS England about the stockpiling of medicines and supplies, which was most people’s big fear. The stockpiling that has taken place mitigates against that risk."
She added: "The biggest concern really is if people don’t believe or trust that information. We’ve put messages out to GP surgeries and pharmacies to be aware of that.
"Giving patients more than they actually need would cut across all the work we’ve been doing."