A Wirral Council spokesperson said it was not known where the families would be relocated pending the results of their asylum claims.
This process is handled by contractor Serco on behalf of the Home Office.
In her letter to Eagle, Basnett said the families “had become part of the fabric of the town” and the decision to “uproot” them had been made without “meaningful consultation with the council, local MPs, or the residents who will be directly affected”.
She said residents had expressed “clear opposition” to the change, citing “concerns over safety, community stability, and the displacement of families who have integrated successfully”.
Protestors have gathered regularly outside the hotel in recent weeks, which Basnett described as “distressing”.
Three people have been arrested in connection with the protests.
Basnett said the changes risked “undermining community cohesion and trust” and asked Eagle to reconsider the decision.
Her letter ended: “I have a duty to act on their behalf, and their overwhelming message is that this change is neither fair nor appropriate.”
Other political parties in Wirral have also written to the Home Office to express their concerns.
However, the former co-leader of the Green Party on Wirral Council said the same hotel had been used to house single men during the Covid-19 pandemic without any issues.
Jo Bird said: “People seeking sanctuary should be welcome on the Wirral.
“The government should process their claims quickly and fairly, so they’re allowed to work, pay rent and raise their families.”