Mr Robinson apologised to the House of Commons on Wednesday for failing to register his ownership of Roll Center Inc, an American Company, which was revealed in The Independent last week.
However, Mr Hague said yesterday in a letter to the Prime Minister that the apology pre-empted an ongoing inquiry by the Standards and Privileges Committee.
"Such an apology by a serving minister is highly unusual if not unprecedented and merely confirms that the reputation of the Paymaster-General is now irreparably tarnished," Mr Hague wrote. "It is time you stopped clinging on to one of your cronies and had the courage to sack the Paymaster-General."
The shadow Chief Secretary to the Treasury, David Heathcoat-Amory, added to the catalogue of complaints against Mr Robinson in a letter to Sir Gordon Downey, the Parliamentary Commissioner for Standards.
Mr Heathcoat-Amory said he found it "inconceivable" that Mr Robinson's business relationship with Robert Maxwell was unpaid, despite a ruling by the committee to that effect.
"The sanction they recommended in respect of the other infringements might have been more severe if this separate and additional breach had been known," he wrote.
In a separate development yesterday, the Standards and Privileges Committee recommended a new independent committee to hear appeals by MPs who are found guilty of offences.
It also said a legally qualified assessor should be appointed to assist the new Parliamentary Commissioner for Standards, Elizabeth Filkin.
Last year, the Tory MP Ann Widdecombe resigned from the committee because she believed her Conservative colleague Neil Hamilton had not had a fair chance to defend himself against allegations that he took cash from Mohamed Al-Fayed, owner of Harrods.Reuse content