A number of experts have called on the government to provide "clear advice" to the public on the matter.
Face coverings should be replaced when becoming damp because the water restricts the airflow, impacting on the way it filters.
Currently, people in the UK are required to wear face coverings in a number of places - including shops, supermarkets and hospitality venues when customers aren't drinking or eating, as well as private taxis and public transport.
Face coverings are not required when outdoors.
Tim Spector, a professor of genetic epidemiology at King's College London, told The Times: "It would now be useful if clear advice were issued to the public.
"Masks need to be changed regularly and this is particularly important to understand in damp and wet weather."
Guidance from the WHO states: "All masks should be changed if wet or visibly soiled; a wet mask should not be worn for an extended period of time. Replace masks as soon as they become damp with a new clean, dry mask."
Its also says three-layer fabric face masks should be worn, which should be used and disposed of appropriately to ensure they are as effective as possible against COVID-19.
The Department of Health and Social Care also advises that people should "change the face covering if it becomes damp or if you've touched it".
Professor Karol Sikora, former chief of the WHO's cancer programme, told The Times: "Moisture makes masks porous and because of this all types of mask are essentially vulnerable in damp weather."
He added that people need to "be given clear advice by the authorities".
Aseem Malhotra, a consultant cardiologist, said: "It is obvious that masks will get damp as people shop and travel in bad weather.
"There has been no public campaign to make people aware that this can make their masks ineffective."
In France, where face masks being worn outdoors is required, people are encouraged to carry a second mask in case it rains.
A recent report by the Scientific Advisory Group for Emergencies (SAGE) found that over half of people use disposable face coverings.
It also said that only one in eight people using reusable coverings have been washing them correctly.