Conservative MP Marco Longhi said ministers were stoking public fury by failing to meet key pledges to address immigration problems.
In an Express & Star interview Boris Johnson insisted Britain would take back control of its borders by cracking down on people traffickers. And last night the PM called on France to agree to "take back" people who cross the Channel to the UK.
It comes as 27 people trying to reach Britain drowned when their boat capsized near Calais on Wednesday, while the total number of migrants crossing the Channel this year has topped 25,000 – almost three times more than in 2020.
Shadow City Minister Pat McFadden, MP for Wolverhampton South East, warned that more deaths at sea were likely to follow unless Britain and France co-operate to solve the problem.
Dudley North MP Mr Longhi said dealing with immigration should be Mr Johnson's number one priority.
He said: “People in this region voted for Brexit and then for Boris as Prime Minister to get Brexit done and take control of our borders and our laws.
"Every dinghy leaving France is a very visible expression of our failure to deliver on that.
“People are frustrated, and if it is not sorted out there will be a price to pay at the ballot box.”
He said he wants Britain to follow the Australian model of opening offshore processing centres, where illegal immigrants could be sent to instead of being brought ashore in the UK.
"We need to send an uncompromising message to economic migrants that 'you will not succeed' if you try and come to Britain," he said.
"We need to be giving a cast iron commitment to delivering this type of scheme."
He was also critical of the French authorities, who he accused of assisting migrants to head for Britain.
Mr Johnson has vowed to “break the business model of the gangsters” who were behind the huge rise in attempted migrant crossings.
Others have pointed the finger of blame towards Europe, with one MP warning the French were in danger of turning the Channel into a graveyard.
It comes after Home Secretary Priti Patel told the Commons she had spoken to her French counterpart and offered to put more officers "on the ground" as part of a continued push for joint patrols of the Channel.
She said Wednesday's incident was a "reminder of how vulnerable people are put at peril when in the hands of criminal gangs".
Responding to the crisis, Shadow City Minister Pat McFadden, Labour MP for Wolverhampton South East, said: "We cannot have our asylum and immigration policy being driven by people traffickers who are exploiting people and preying on their desperation.
"If the current situation continues we are likely to see more loss of life at sea."
He said solving the issue would take "proper sustained co-operation" between Britain and France and possibly other countries too.
"We can’t afford a descent into point scoring or a mutual blame game on either side of the Channel," he added. "The only people that will suit are the people traffickers.
"We are not alone in trying to deal with this issue. It is important to remember that countries like France and Germany receive significantly more asylum applications overall than the UK.
"The Government must try to get a grip because it certainly doesn’t have one right now.
"They must pursue the traffickers organising this process and put the necessary co-operation in place with other countries to try to stop the rise in people taking to the seas in these dangerous small boats."
Shrewsbury & Atcham MP, Daniel Kawczynski said: "I very much hope this terrible human tragedy compels the French authorities to finally start to take action, police their coast line, and pursue these criminal gangs making a lot of money out of endangering people's lives and creating a lot of human misery."
He added: "Unless the French act they will start to turn the channel into a graveyard and they are not acting sufficiently in order to prevent these people smugglers from endangering people's lives.
"They can use drones, then can use helicopters to police their shores to prevent this from happening and clearly the French government are not doing what is needed to prevent these tragedies from occurring."
Mark Pritchard, MP for the Wrekin, said: "The people smugglers must be stopped and their evil supply chains disrupted at home and abroad.
"The root causes also need to be addressed: poverty, persecution, war, famine, corrupt and failed states; all feed into mass migration at different times. What happens abroad very much matters here in the UK."
Telford MP Lucy Allan said: "This is a terrible human tragedy. The Home Secretary has worked tirelessly to solve the problem of illegal channel crossings. We must do all we can to assist the French in patrolling their beaches to prevent these unsafe boats leaving the French shore and for any migration to take place through legal mechanisms."
Warley MP John Spellar said the tragedy "emphasises the need to crack down on the evil people smugglers who are profiting from misery".
In an emergency debate in the Commons yesterday Tory MPs told Emmanuel Macron it was "within his gift" to end the crisis by allowing the deployment of British police officers on the French coast.
Wolverhampton-born former Cabinet minister Robert Jenrick said the French President could "bring this to an end now", while Sir Iain Duncan Smith called on the Government to exert the "greatest pressure" possible on Paris to do more.
Amid a growing row between British and French authorities, Mr Macron insisted France was "totally mobilised" to stop migrants crossing the Channel and warned Mr Johnson not to "exploit" the latest tragedy.
Mr Johnson conceded there had been "difficulties" persuading the French "to do things in a way that we think the situation deserves".
In a letter to Mr Macron, he said a return agreement for those who cross the Channel would have "an immediate and significant impact".