Sir Jeffrey adds his party "like a lot" of what was in the Queen's Speech, adding that Tory policies put forward during the election campaign that caused them concern are "fading into the background".
What was in the speech?
But she did say the government is looking forward to a planned state visit by the Spanish royal couple set for July.
The new bill will replace the Data Protection Act 1998. May is promising a government "that consults and listens".
Warning of an "unprecedented" threat from terrorism in the wake of attacks at Westminster, Manchester and London Bridge, Mrs May announced a review of counter-terrorism strategy to make sure police and security services have "all the powers they need to protect our country".
There was further criticism of the US President after Mr Trump attacked Mayor Sadiq Khan about his response to the latest terror attacks on the capital.
The 91-year-old monarch carried on with her royal duties at the ceremonial opening of the new Parliament despite the announcement that her husband, Prince Philip, had been hospitalized.
After the Tories' disastrous General Election showing saw the party lose its Commons majority, Mrs May sought a "confidence and supply" deal with the DUP to prop up her minority administration. Prince Charles accompanied her for the speech.
China In Talks To Pressure North Korea After Student Death
It was also unclear how Trump's comment would be interpreted by the Chinese delegation during the day-long dialogue on Wednesday. North Korean threats, trade tensions and global terrorism are expected to be among the issues discussed at the inaugural U.S.
In written remarks prepared for the first day of Parliament, the troubled Prime Minister began trying to undo some of the key messages from the Conservatives' election campaign, saying that social care would be addressed and that every school should be fairly funded.
An Immigration Bill abolishes European Union free movement rules after Brexit and provides a framework for the United Kingdom to control migration while attracting "the brightest and the best".
The failure to bridge differences casts doubt on Mrs May's ability to get her Queen's Speech through Parliament, with senior minister Damian Green acknowledging it is possible that no agreement will be reached in time for the crunch Commons vote on the package on June 29.
Labour leader Jeremy Corbyn has already said that his party could vote against the Queen's Speech and even offer up some amendments.
City deals to give local councils in Northern Ireland greater economic powers and contracts for the province's firms to benefit from higher defence spending have also been raised.
The Queen's Speech usually sets out the government's legislative plan for the 12 months ahead, but this year's is different.
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