The government's Nationality and Borders Bill will only bring more "chaos and delay" to the UK's "dysfunctional" immigration system, Amnesty International has said.
The bill passed its second reading in the Commons on Tuesday evening by 366 votes to 265.
It would allow the UK to send asylum seekers to a "safe third country" and to submit claims at a "designated place" determined by the secretary of state.
It would also mean anyone knowingly arriving in the UK without permission would be committing a crime, and Border Force officers would have the power to turn back migrant boats using "reasonable force if necessary".
But Steve Valdez-Symonds, Amnesty UK's refugee and migrant rights programme director, said: "Criminalising people just for trying to reach a place of safety is morally and legally indefensible.
"People cross the Channel and put themselves in serious danger because there are simply no safe alternatives open to them.
"Unless MPs drastically amend this bill, we will end up with even more chaos and delay in our dysfunctional immigration system."
Home Office minister Victoria Atkins told Sky News the government wanted an immigration system that is "firm but fair", with "safe routes for people to come legally" alongside "cracking down on these criminal gangs that are exploiting people's wishes to come to this country".
She told Kay Burley that many of those reaching the UK are not claiming asylum in the first safe country they enter.
"We've only to see the movement patterns across the EU towards the French beaches and then the boats coming across to see that people don't seem to be taking up the opportunity to claim asylum and seek safety in other countries in the EU that are perfectly safe," Ms Atkins said.
"That's the message we've really got to land with people. That if you're landing in the EU it's a safe set of countries, of course it is. Please, that is where you should be seeking asylum."
Home Secretary Priti Patel says the bill will address the UK's "broken asylum system" as record numbers of migrants risk travelling on small boats across the Channel.
Ms Patel is due to appear before the Commons Home Affairs Committee this morning to update MPs on the situation.
There have already been more people crossing the Channel on small boats this year so far than there were in all of last year, according to Home Office data compiled by the PA news agency.
At least 287 migrants reached the UK on Tuesday, bringing the year's total to at least 8,452.
During 2020, 8,417 people crossed the Dover Strait aboard small boats.
On Monday, at least 430 people arrived by small boat in the UK, a new record for a single day.
Tim Naor Hilton, chief executive at Refugee Action, said the growing number of crossings "shows the government's get-tough-quick schemes do not work".
He added: "Criminal smugglers prey on refugees who have little choice than to put risk their lives in rickety boats because ministers refuse to create more routes to reach safety here.
"And the government's cruel anti-refugee bill will do little to stop the boats. It is unworkable, unlawful and will end up an expensive disaster that criminalises people who are simply asking for our help."
Dan O'Mahoney, clandestine channel threat commander for the Home Office, said: "There is an unacceptable rise in dangerous small boat crossings across the channel because of a surge in illegal migration across Europe.
"The government continues to take steps to tackle the unacceptable problem of illegal migration through the Nationality and Borders Bill which will protect lives and break this cycle of illegal crossings.
"The government is also continuing to return those with no legal right to remain in the UK."
Also on Tuesday evening, the Home Office announced that Britain is to give France another £54m to prevent crossing, following an agreement between Ms Patel and French Interior Minister Gérald Darmanin.