Labour MP Lisa Nandy, in an interview with the Observer, cited the Homes for Ukraine scheme’s “lengthy forms and the documents you need to prove your identity and residency” as a big issue for the program to succeed.
She said: “Unless urgent steps are taken to address this, we will see very small numbers of people taking up this offer and a lot of the public’s generosity squandered.”
Under the scheme, UK residents can individually sponsor a Ukrainian national’s visa.
Launched on Tuesday, some 100,000 people registered interest within the first day.
Applications opened on Friday.
Housing and Communities Secretary Michael Gove said there is no limit to how many Ukrainians can enter the program.
Each household taking in one refugee will be offered £350 a month, tax-free, and will not be expected to provide food and living expenses – though they can choose to offer this.
One of the current most evident limitations of the scheme is that Britons ready to open their home to a refugee rely on knowing a named individual from Ukraine they want to help.
According to Mr Gove, this is a temporary condition intended to get things “up and running as soon as possible”.
Ms Nandy condemned the Government’s little to no collaboration with councils and charities when setting up the scheme.
She said: “I met with a group of councils just before Michael Gove came to make a statement about the scheme to the Commons on Monday and not a single one had been contacted.
“Councils are desperate to help, but their concern is how to make this scheme work in practice.”