The Met Office warned of "significant disruption and dangerous conditions due to extremely strong winds", adding that roofs could be blown off, trees uprooted and power lines brought down.
Roads, bridges and railway lines have already been hit causing delays and cancellations to bus, train and ferry services.
Another red warning was already in place for parts of Cornwall and south Wales.
"Please take precautions. Please stay safe," Home Office minister Damian Hinds told Times Radio.
"It is unusual to have a red weather warning. It is very unusual to have two."
Trains into the capital were already running limited services during the morning rush hour, with speed limits in place.
National Highways also issued a severe weather alert for strong winds covering the whole of the country's strategic road network from 6.00am to 6.00pm.
The agency said there was a "particularly high risk" for high-sided vehicles.
Key river crossings including the Severn Bridge in southwest England and the QEII Bridge south of London were also closed.
The arriving storm forced Prince Charles, the heir to the throne, to postpone a trip to South Wales on Friday "in the interests of public safety", his office said.
Ireland's meteorological office also issued an alert for Storm Eunice, warning of "severe and damaging winds" and the possibility of coastal flooding.
Another storm, Dudley, caused transport disruption and power outages when it hit Britain on Wednesday, although damage was not widespread.
The UK government on Thursday held a meeting of its emergency "COBR" committee to discuss the response to the two storms.
Prime minister Boris Johnson expressed sympathy for thousands of residents left without power in northern England by Dudley.
Asked about further support ahead of the arrival of Eunice, he told reporters, "The army is on standby".
Schools in the path of the storm announced on Thursday they would shut for the day and residents were urged to remain indoors. Heavy snow was also forecast in Scotland and northern England.