Plans to ensure more local councils do their fair share to provide accommodation for asylum seekers will win the backing of the upper house of parliament now that VVD senators have said they will vote in favour.

The legislation is “not the best in the world” and will not solve all the problems, said VVD senator Marian Kaljouw. “But we did not want to leave the mayors, the king’s commissioners, Ter Apel, the COA refugee settlement agency and the IND immigration service in the lurch.”

The actual vote takes place next week but the decision by the 10 VVD senators to back the bill means it will now pass with at least 46 of the 75 senate votes.

Their decision is notable because VVD leader and justice minister Dilan Yesilgöz earlier dropped her support for the legislation, drawn up by her own junior minister and fellow VVD politician Eric van der Burg.

She also tried to persuade the new look lower house of parliament to pressure the senate to delay its deliberations because there is no longer majority support for the measure in the wake of the November general election.

PVV leader Geert Wilders, whose far right party was the big winner in the November vote, reacted to the VVD change of heart on social media by saying “heavens” and told NOS he was “shocked”. Far right senators said the VVD’s position is a “betrayal”.

Supporters of the measure have welcomed news of the VVD’s decision. “We can now start to solve the terrible situation in the centres,” said Jaap Velema, mayor of Westerwolde in Groningen, which is home to the overcrowded Ter Apel reception location.

Wouter Kolff, the mayor of Dordrecht and chairman of the local authority safety board Veiligheidsberaad said the new legislation will reduce the likelihood of people ending up in emergency accommodation.

“Now we can start a proper discussion about the number of arrivals as well as how we can offer people who do come here a proper roof over their heads,” he said.

Research published by broadcaster RTL Nieuws on Tuesday showed that almost half of the Netherlands’ 342 local authority areas have not provided any accommodation for refugees over the past 12 years.

According to a poll by current affairs show EenVandaag, 51% of the population back the legislation and 13% are undecided. In addition, 57% of VVD voters also now support the plan.