The All Party Parliamentary Group on Social Integration says migrants should be treated like Britons-in-waiting who are expected to eventually gain citizenship, instead of being seen as security threats.
Newcomers are increasingly living parallel lives and anti-immigrant rhetoric is making it harder for people to fully integrate in British life, the MPs say.
The APPG says there should be a legal duty on councils to promote integration and the Government must encourage “meaningful social mixing” between immigrants and Britons.
Businesses that employ large numbers of immigrants should pay a levy, with the cash being used to help ease the strain of migration on communities, the MPs suggest.
Labour MP Chuka Umunna, chair of the APPG, said: “The demonisation of immigrants, exacerbated by the poisonous tone of the debate during the EU referendum campaign and after, shames us all and is a huge obstacle to creating a socially integrated nation.
“We must act now to safeguard our diverse communities from the peddlers of hatred and division while addressing valid concerns about the impact of immigration on public services, some of which can contribute to local tensions.
“We must start by valuing the contribution of all ethnic and minority communities to the UK. Rather than being seen as security risks, immigrants should be viewed as Britons-in-waiting, keen to participate in their community.
“The best way to do this isn’t to leave newcomers and their communities to sink or swim, but to offer migrants more support to integrate into our society.”
But the pro-Brexit pressure group Leave Means Leave accused Mr Umunna of being “in denial” over the referendum result and why people voted for Brexit.
Richard Tice, co-chair of the group, said: “There is nothing ‘poisonous’ about wanting to take back control over Britain’s borders, in fact he should be ashamed to suggest there is.
“He (Mr Umunna) clearly has no regard for the 800,000 young people aged 16-24 who are not in employment, education or training because of the ease of cheap labour from the EU.
“Freedom of movement from the EU into Britain is a system which discriminates against residents of non-EU countries – not to mention the £3,500 each unskilled migrant costs the British taxpayer every year.
“Chuka is in complete denial about the referendum result and is trying to retain a form of freedom of movement which is completely against the democratic will of the British people.”
The APPG came up with its findings by visiting areas of high immigration in Yorkshire, Lincolnshire and Dagenham, as well as speaking with a number of experts.
Critics of the group accused it of attempting to continue freedom of movement through the back door when it released interim findings earlier this year calling for a regional immigration system.
In its full report, the group said it would be “perfectly plausible” for ministers to implement a regionally-led system for non-EU immigration while “continuing to subscribe to some form of freedom of movement” after Brexit.
Under a regional system, local politicians would be able to assess the impact of migration on public services and community cohesion, the report says.
Regional immigration authorities would also be able to create a certain number of visas to meet specific employment needs, but workers arriving under the scheme would be expected to remain in the area for two or three years before they are able to move elsewhere.
August 25th, 2017: Sky News