When summoned to the House of Commons on Thursday, May said the Passport Office was receiving 350,000 more applications for passport applications and renewals than normal for this time of year.
He told MPs that 3.6m applications for passports had been received since 1 January, 1.9m of them since 1 April.
On Monday, a sign on the consulate door said that it was no longer taking applications for passports or visas.
Human Rights Watch said Monday that at least 19 former student activists' applications for passports had been turned down.
The home secretary has used the royal prerogative 14 times to refuse applications for passports or confiscate them.
Citizens along the United States-Mexico border whose applications for passports were sent to a bureaucratic black hole because their births were attended by midwives will be able to reapply.
Transactional services provided by the government include road or income tax, and applications for passports, visas, driving licenses, benefits, grants or loans.
Earlier their applications for passports had been denied.Although Mr Liu and his relatives are suffering, the picture for other dissidents who signed Charter 08 has been mixed.
Employees at the Passport Office in Liverpool, one of seven centres in Britain, were told on Tuesday that passport workers were processing first-time applications for passports from overseas dating back to 31 March.
They include payments for road tax or income tax, applications for passports, visas, driving licences, jobseeker's allowance or student loans, as well as providing or requesting information on a whole range of matters from income to apprenticeship vacancies.
