The UK Members of Parliament (MPs) and peers said that migrants should have learnt English before they arrive in the UK or should attend English language classes as soon as they arrive.
BBC quotes members of all parties as saying unanimously that English was crucial to participate totally in the British society and economy.
They were also of the view that ministers should allow different regions of the UK to draft their own immigration policies.
The members referred to the use of a similar model in Canada, where governments of each province could determine region-specific needs for immigrants.
They also added that visas could be exclusively issued for specific regions or some exclusive sectors.
Chuka Umunna, Labour MP, chair of the all-party group, said that though both native and immigrants had a role to play integration, Britain had an obligation to fund language classes in English.
Meanwhile, the government announced that £20 million was being spent on English language provision.
According to Umunna, a meaningful adaptation programme would be required when the rules are amended after Brexit comes into effect.
But the Home Office said that it had no plans of introducing local visa arrangements.
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