A group of Conservative lawmakers called on British Prime Minister Rishi Sunak on Monday to do more to cut immigration, saying he risked further eroding the trust of voters who lent the party their vote in 2019 if he failed to take action.

The group of lawmakers, many elected for the first time in 2019 in traditionally opposition Labour-supporting regions in northern and central England, is just one faction of the party putting pressure Sunak to act more decisively to try to lift the Conservatives' flagging poll ratings.

When Sunak came to power last year, he made five pledges to turn around the electoral fortunes of his governing party, including stopping "the small boats" or tackling illegal migration to bring down the numbers.

But on an earlier Conservative promise made at the 2019 election to cut net migration, the British leader has been more reticent, committing only to bringing down levels of legal migration without giving any targets.

In a report, the so-called New Conservatives group of over 25 lawmakers out of the more than 300 in parliament issued a 12-point plan to cut immigration, including closing temporary visa schemes for care workers, limiting students from staying in Britain after graduating and capping the number of refugees.

"Without swift action to get migration under control, the Conservative Party will further erode the trust of hundreds of thousands of voters who lent the party their vote in 2019," said the report, written by lawmaker Tom Hunt.

"The Conservatives need to achieve (or at least be on course to achieve) a reduction of around 400,000 in LTIM (long-term international migration) if they are to save face by the time of the next general election."

A spokesperson for the interior ministry said the government remained committed to reducing overall net migration, pointing out its measures to stop the boats and remove the right for most international students to bring family members.

"We will continue to strike the right balance between supporting the UK economy through skilled worker visas and upholding our commitment to reduce migration over time," the spokesperson said.

Under Boris Johnson, the Conservatives won a large majority in 2019, winning over thousands of traditionally Labour-supporting voters with a promise to get Brexit done and to reduce the numbers of migrants arriving in Britain.

Several lawmakers who won those seats fear they will lose their jobs after a national election expected next year, with opinion polls handing Labour around a 20% lead over their party.

Sunak faces a raft of struggles to keep his agenda on course, with his five pledges - including bringing down waiting times in Britain's health service and halving inflation which is stubbornly high at 8.7% - looking to difficult to achieve.