Shadow culture secretary Ivan Lewis said the government should introduce a wider public interest test and allow regulators to apply a fit and proper persons test.
Glover's takeover was initially agreed last week but was subject to the RFL's final written confirmation that he had passed a fit and proper person test.
The group also called for a tightening up of the FA's Fit and Proper Persons Test for potential club owners, saying that debt plans should be taken into account, and that proposed takeovers should be rejected "where it is considered against the long-term interests of the club".
The Conservatives said it was evidence of the need for "proper controls" on immigration - including a cap on work permits and language test for those who want to move to Britain to get married.