Local MP Connor Rand has raised the issue of the Cresta Court in Parliament as the government said it remained "committed" to ending the use of hotels for asylum seekers.
Last month the Vine Hotels-owned hotel was abruptly closed in order to house up to 300 all-male migrants while their claims for asylum were assessed.
Local residents have raised security fears following the migrants' arrival and a protest took place close to the hotel on Saturday, as well as two residents' meetings at local churches.
Dame Angela Eagle, Minister of State for Border Security and Asylum, confirmed in the House of Commons today that the Cresta Court was one of 14 new migrant hotels to have opened since Labour won the general election in July, taking the total number across the UK to 220.
Labour had promised to close all asylum hotels in their manifesto, but Dame Angela said they did not commit "to close all asylum hotels within four months".
Instead, she laid the blame for the current situation at the door of the Conservatives, saying that when they returned to power in the summer they found a backlog of 116,000 asylum seekers going back two years.
She said the system had "ground to a standstill" because of the Tories' now discontinued Rwanda policy.
"We inherited an unholy mess from the party opposite," she said.
"We remain absolutely committed to ending the use of hotels for asylum seekers."
Speaking in the debate, newly elected Labour MP for Altrincham and Sale West, Connor Rand, said he was "pushing" for the cases of the Cresta Court migrants to be "prioritised" so that the situation could be resolved "as soon as possible".
He said: "I know that this government understands that using hotels to house asylum seekers is bad for communities, bad for the taxpayer and ultimately bad for those themselves seeking asylum.
"And whilst those on the benches opposite who broke our asylum system wash their hands of the consequences now, can the minister outline the progress the government is making on clearing the backlog that they created, so we can stand down hotels, including prioritising the processing of those housed at the Cresta Court hotel in my constituency?"
He later added: "I’m regularly speaking with Home Office Ministers and officials to voice the concerns that residents have about Cresta Court, and I’ll keep pushing for the cases of those at the hotel to be prioritised for processing so this situation can be resolved as soon as possible."
Dame Angela claimed that asylum claims were not being processed at the rate of 10,000 a month, 10 times the previous rate.
She said: "We are prioritising getting the system up and running again so we can have throughput through our asylum accommodation estate.
"The fact that the system had ground to a complete halt, that there were 90,000 unprocessed cases in that system when we came into government, has meant that there are lags and delays in getting it up and running.
"I've just explained to the House that we've gone from making 1,000 asylum decisions a month to 10,000. The system is beginning to get flow through, and as that flow through happens, we will exit from hotels."
