Northern Ireland will see a dry start but then see strong winds and heavy rain, and the south-east will remain damp throughout the day and into overnight.
As winds ease off later on Saturday, some hill snow is forecast in central and southern parts of England and into Wales, Mr Burkill said, before calmer conditions on Sunday.
Delays for high-sided vehicles on exposed routes and bridges are likely and some short term loss of power and other services is possible, said the Met Office.
Parts of the country could also experience hail and thunder.
Later, however, the clouds will move towards Scandinavia with exception of the south.
A British Airways plane has been filmed being forced to abandon its landing as strong winds from Storm Erik batter the UK.
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He also added: "It will be a brighter second-half of the day for Wales, south-west and northern England with a few showers thrown into the mix as well".
"Because of the cold air, this could fall as snow on higher ground in Scotland and England on Sunday".
The Met Office's wind warning, which was in place until 15:00 BST on Saturday, has now been cancelled.
Storm Erik came with a status orange weather warning for Donegal, Mayo and Galway and wind gusts at times were really powerful.
On Friday morning a 50-year-old died on the A384 in Buckfastleigh, Devon, and in Wales, a van driver was killed after he collided with a fallen tree on the B4306 between Pntyberem and Llannon in east Wales.
A yellow weather warning has been issued Norfolk this weekend, with gusts of up to 55mph potentially hitting parts of the region.
Wind speeds of 69mph were recorded in Powys, Wales, and 68mph in Avonmouth, Bristol, while 50mph winds were expected inland, Met Office meteorologist Simon Partridge said.
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