Millions of people are being advised to stay at home and rare red weather warnings – meaning danger to life – have been issued with winds of 100mph set to batter parts of the country.
An amber warning of wind has been issued for Doncaster and travel across the country is expected to be hit as a result, along with power cuts and flooding.
Earlier, the Met Office has issued a second rare red weather warning to cover London, the south-east and east of England.
A red warning - meaning there is a danger to life from flying debris - is already set to cover parts of south-west England and south Wales.
BBC Weather said it "could well be one of the worst storms in three decades".
There is an amber warning for wind covering all of England south of Manchester and Wales until 21:00 with gusts of up to 80mph
A yellow warning for snow is also in place for much of Scotland, Northern Ireland and northern England from 03:00 until 18:00
A yellow warning for wind in the Midlands, north-east England, north-west England, parts of Northern Ireland and parts of Scotland from 07:00 and 18:00 with gusts of up to 70mph
A yellow warning for wind covering London, south-east England, south-west England, Wales and parts of the West Midlands from 06:00 to 18:00 on Saturday
BBC Weather meteorologist Ben Rich said he expected Eunice to "cause damage, huge disruption and coastal flooding" - but he said it was "impossible to know exactly how bad this storm is going to be".
Hundreds of schools across the country have been closed, all train services in Wales have been cancelled and the Army has been put on standby in some parts of the country as hurricane force winds tear across the country.
People have been advised to travel only if essential.