The figures were released by the Home Office in a written parliamentary answer.
Commons Home Affairs Select Committee chairman Keith Vaz told the Times, which analysed the figures: "It is deeply concerning that a third of all asylum applications have been made by illegal migrants and overstayers.
"The very principle of seeking asylum is that you feel persecuted at the time you arrive, not saying you feel persecuted after arriving illegally or for different reasons and then remaining in the country until you are apprehended.
"This is a significant clog in the immigration system, and we should ensure that this is not to the detriment of vulnerable people with a legitimate claim of asylum. It is one thing for the Government to say it's tough on illegal immigration - it's another to actually take control of issues like these."
A spokeswoman for the Refugee Council said delayed asylum claims were not necessarily false.
Advocacy manager Anna Musgrave said: "It's misguided to believe that asylum claims which aren't made immediately are somehow invalid.
"People's circumstances can change as in the case of Syrian students and business people who were in the UK when war erupted in their country and they found themselves unable to return when their visas ran out.
"Obviously decisions on asylum claims must be based on whether or not someone's life is at risk, not on arbitrary timescales."
