Around 2,000 refugees have arrived at the Austrian border from Hungary so far, Austrian police say, adding that the number could more than double by the end of Saturday.
Hans Peter Doskozil, chief of police in the Austrian province of Burgenland, said two special trains had been arranged to take migrants from the border town of Nickelsdorf to the capital Vienna, after they had been brought by bus by Hungarian authorities.
However, he claimed that Hungary was refusing to let Austrian buses enter Hungary to pick them and deliver them to the trains, meaning they had to walk in rain and darkness.
"Our biggest problem is that the Hungarians - after checking back with Budapest - are refusing to let our buses enter their territory and pick up the refugees," he said.
He added: "We offered them that they can bring the refugees directly to the trains, or to the shelter [on the Austrian side], but they just stop the buses on the Hungarian side, everyone has to get off in the rain."
It'll be largely dry and bright across many parts today with plenty of sunny spells, particularly in the north.
The remnants of a weak front with patchy rain and drizzle will clear the far south through the first part of the morning with cloud breaking up behind.
It will feel cool with the northwesterly breeze persisting, keeping temperatures down to a maximum of 18C (64F).
Passengers on one of the country's busiest rail lines were forced to deal with hours of delays as a knock-on effect of cable theft.
Customers on the Virgin Trains East Coast main line were informed on the tannoy system that the disruption was caused by the "vandalism" at Darlington which in turn caused signalling problems.
Some services were replaced by buses, while on others passengers were delayed by up to 60 minutes even after the problem had been fixed.
Anyone delayed by more than 30 minutes can apply for compensation via the Virgin Trains website, the operator said.
Hundreds of migrants and refugees are beginning to arrive at the Austrian border after Hungarian authorities laid on buses to carry them there.
Austria and Germany have both said that they will grant them access, regardless of European Union rules which are meant to restrict the movement of unregistered migrants.
Hungary's decision to transport people to the border followed days of chaos in the capital Budapest, which resulted in more than a thousand attempting to get there by foot.
The crowd was led by a one-legged Syrian man as it travelled along the main highway to Vienna, and could be heard chanting "Germany, Germany!"
More than 140,000 migrants have been recorded entering Hungary so far this year through the EU's external border with Serbia, and the decision to aid thousands in reaching Austria marked an embarrassing climbdown for the country's right-wing government.
Hundreds of migrants and refugees have been pictured aboard buses headed for the Austrian border after days of chaos in Hungary.
Up to 1,500 were expected to arrive at a reception centre on the Austrian border overnight, the Austrian Red Cross has said.