After days of devastation to Britain’s transport network, Sunday morning dawned at the UK’s busiest railway station with an unfamiliar air of normality. The first trains trundled off to suburban south-west London on schedule, while passengers on longer-distance services to Portsmouth and Weymouth are enduring the expected bus replacement services because of scheduled engineering work.

South Western Railway plans to run a normal Sunday service, though it is the exception; most train operators are warning travellers of some disruption.

Virgin Trains East Coast said: “Customers are advised not to travel today unless absolutely necessary. Services are expected to be extremely busy.”

In Wales, no trains are running west of Carmarthen, while the line from Cardiff to Shrewsbury is closed. Arriva Trains Wales said: “The situation is extremely changeable and train services continue to be severely impacted with extensive cancellations and last minute significant changes.

“The start of service on Monday 5 March is also likely to be severely impacted.”

Six Eurostar services are cancelled on Sunday: two return journeys from London to Paris, and a round trip to Brussels. One service to and from Paris is cancelled on Monday. The cross-Channel train operator warned: “If you’re travelling today or tomorrow you might arrive at your destination with a delay of up to 60 minutes.”

The GWR lines in the Cotswolds, from Swindon to Gloucester and Oxford to Hereford, have closures and disruption.

In Devon, the coastal line between Exeter and Teignmouth is subject to speed restrictions. CrossCountry trains in the South West are being hit “due to a shortage of trains following damage by snow and ice”.

Coastal resorts are gradually being reconnected to the national rail network. Newquay in Cornwall, Cromer in Norfolk and Skegness in Lincolnshire will see their first trains moving for days. But the Norfolk and Suffolk branch lines from Norwich and Ipswich to Great Yarmouth and Lowestoft remain closed.

In the northern half of Britain, lines across the Pennines from Leeds to Lancaster and Carlisle remain closed, as well as the route paralleling Hadrian’s Wall from Hexham to Carlisle. The West Coast main line remains closed across the Scottish border, though a bus replacement service will operate between Carlisle and Glasgow.

While many rural roads remain closed, almost all the nation’s trunk routes are now open. One of the last to be cleared was the A66 west from Scotch Corner in North Yorkshire. Highways England said: “There are some power lines which have been brought down around the A67 in Bowes, which may require closures prior to repairs.”

In the skies, passengers flying in and out of Birmingham airport continue to experience problems. The early flight on Ryanair from Dublin was diverted to Manchester, while Wizz Air’s flight from Warsaw landed at Liverpool. Some Sunday afternoon departures were running up to six hours late.

Off track: Wizz Air flight from Warsaw to Birmingham, diverted to Liverpool (FlightRadar24)

Elsewhere, the issues are largely to do with planes and crews being out of position after days of turmoil. The problem is still very evident in Dublin, which closed completely on Friday and had a difficult day on Saturday. BA’s first flight from the Irish capital to Heathrow was cancelled.

TUI’s flight from Tenerife to Manchester on Sunday afternoon is delayed six hours, while the Goa to Gatwick service is expected to operate 13 hours late.