The UKHSA issued a yellow cold-health alert covering northern regions of England as colder air feeding from the north could lead to wintry showers in parts of the UK.
Meteorologists say that towards the end of the week, there is a possibility of snow across parts of the south. However, this is not guaranteed.
Met Office deputy chief meteorologist David Oliver said: "After some rain on Monday, conditions will turn mainly dry in the south for a time before a very uncertain period on Thursday and Friday for the southern half of England and Wales.
"The weather models are highlighting several possible solutions from very wet to mainly dry, with a mainly dry picture the most probable outcome at present.
"However, some models include the prospect of an area of low pressure developing and moving in from the south or southwest."