Registrars should be given the power to refuse to conduct marriages they believe are "bogus", MPs said in a warning that more needed to be done to counter what had become an immigration scam "industry".
The number of suspect couples being referred annually to the Home Office has more than doubled in three years to 2,135 and the true figure is almost certainly far higher due to under-reporting, the Commons Home Affairs Committee said.
But registrars received too little information from immigration officials about what action was being taken, leaving them obliged to officiate at ceremonies they believed to be fraudulent and should be give more discretion to act unilaterally, it concluded.
The call for more action - including well-publicised prosecutions and asking embassies representing the worst-offending nationalities to issue warnings - followed a warning over Government failures by the independent chief Inspector of Borders and Immigration.
John Vine told the committee last month that there was "widespread abuse" and that officials did not know the true scale of the problem which represented "one of the biggest potential threats to immigration control".
He said there was an "almost complete absence of prosecution and enforcement activity" in individual cases and that greater resources needed to be channelled into tackling the issue.
A Home Office estimate of between 4,000 to 7,000 cases a year probably understated the scale of the problem, he said.
The most common cases involve individuals from outside the European Economic Area seeking marriages with EEA residents in order to gain residence rights not just for themselves but for their extended families.
Ministers have recognised that it is a "significant threat" to attempts to control immigration and introduced tougher measures this year such as a longer minimum period between a marriage being announced and a ceremony going ahead and civil-style checks on church marriage.
Portugal, Lithuania, Poland, Slovakia are reported to be the countries whose nationals are most involved at present - though it goes in waves - with some young vulnerable women from Eastern Europe being offered cash and a new life in the UK for taking part.
In 2010 there were 934 reported suspect weddings but that rose to 2,135 by 2013.
Registrars complained that the failure of the Home Office to intervene left them obliged to preside over what they knew to be a "charade", one telling the MPs it was "like being mocked in your own job".
The committee said it was "implausible" that a number of towns and cities which had reported no cases to the Home Office did not have some bogus marriages taking place on their patch when others, such as Manchester, were referring almost one a day.
Pinning the blame partly on inadequate training and patchy relations between registrars and immigration officials who failed to give feedback, the MPs said they were "not convinced the current level of resourcing is sufficient".
"We recommend that the law be changed so that if the Home Office enforcement team do not act on a section 24 report from the Registrar and the Registrar is confident the wedding is a sham, then the Registrar should have the power to cancel the wedding," the report recommended.
"The Home Office should provide training on how to identify potential shams and, most importantly, it should provide full, accurate and timely information to the Registrars to tell them what action is being taken as a result of their reports."
Committee chair Keith Vaz said it was "absurd" the burden of proof presently lay with the Home Office to prove it was not.
Couples applying for residence based on a "proxy" wedding carried out overseas in their absence - as allowed under some countries's laws - should in future have to prove their marriage was legal.
At present, the burden falls on officials to show it is not, wasting resources, the MP said.
Committee chair Keith Vaz said: "There is an industry of deceit in the UK which uses sham marriages to circumvent immigration control.
"The estimated 10,000 sham marriages appears to be increasing at an alarming rate. One sham marriage can provide UK residence rights to an entire extended family who would otherwise have no right to be here.
"The role of registrars is critical. The Home Office should not only provide them with better feedback and training on reporting but also empower them to stop suspicious marriages.
"Data is not being collected in a consistent manner across the UK. We cannot afford for any town or city to become a back door entry to our country. The Government needs to publish the total number of interventions, arrests, prosecutions and removals to prove that action is being taken."
He went on: "It is absurd that we willingly accept as valid, marriages where the two parties do not attend the ceremony.
"This allows an easy ticket into the UK and this proxy marriage loophole must be closed immediately. Without taking these steps the Government will never get a firm grip on a situation which is spiralling out of control."
The committee also called for the deportation of foreign prisoners to ease pressure on overcrowded jails should be speeded up by forcing criminals - on pain of of penal sanctions - to prove their nationality at the point of sentencing.
And it hit out at "unacceptably slow" efforts to deal with a backlog of asylum cases that was now not on course to be cleared until 2019.
Shadow immigration minister David Hanson said: "This report exposes another crisis at the Home Office of the Home Secretary's making: when will the Home Secretary take responsibility, get a grip and apologise for her shambolic mismanagement which has allowed a sham marriage industry to develop on her watch?
"Six months ago we asked ministers to ensure more was being done to ensure when sham marriages were suspected, action was taken. Last month the chief inspector of borders made clear there was a growing and significant problem that the department just wasn't tackling, and now we have the Select Committee's damning report.
"The Home Secretary can't bury her head in the sand any longer. People will rightly be angry at how it was ever allowed to get this bad. This Government are lurching from crisis to crisis in immigration, and clearly can't be trusted to make it work for the UK."
A Home Office spokesman said: " We are taking ever tougher action, including through the new Immigration Act, to crack down on those who try to cheat our immigration system by abusing marriage laws.
"We are also focusing on cutting out the abuse of free movement between EU member states and addressing the factors that drive European immigration to Britain."