Greg is a qualified Solicitor but is currently non-practising. He lives  in the constituency.

At the General Election of 2001 he was elected Conservative MP for East Yorkshire. He was re-elected for the same seat in May 2005, May 2010 and May 2015. In the 2010 election he more than doubled his previous majority to 13,486 and further increased his majority to 14,933 in 2015, with nearly 51% of the vote.

In October 2001, he was appointed Shadow Deputy Leader of the House of Commons and was given Front Bench responsibility for e-government issues at the Cabinet Office. In July 2003 he was made Shadow Minister for Culture.  In November 2003, he was appointed Shadow Minister for Transport.

In November 2005 he gave up his position as transport spokesman to take over the chairmanship of the House of Commons Procedure Select Committee and was re-elected unopposed to this position in June 2010.

In July 2009, Greg was made one of the members of the new House of Commons Reform Committee, set up by the then Prime Minister Gordon Brown to advise the House of Commons on Parliamentary reform.

In the 2005-10 Parliament, he served on 6 Select Committees, a feat which no other MP, of any party, has achieved.

Since 2001 he has been Chairman of the All Party Parliamentary Historic Vehicles Group.

Along with 3 other Parliamentary colleagues he helped to raise over £1 million for good causes and was presented with an award for so doing by the British Music Industry in 2015.

In July 2011 he successfully piloted through Parliament his Private Member’s Bill, called the Estates of Deceased Persons (Forfeiture Rule and Law of Succession) Act. The Act amends the law of succession in England and Wales where a person disclaims an inheritance; or is disqualified from receiving an inheritance by reason of the forfeiture rule. ‘It makes our law of succession fairer’, Greg said. He is one of only a small number of MPs to have succeeded in changing the law through the Private Member’s Bill procedure.

In September 2012 he resigned as Chairman of the Procedure Committee on becoming Vice-Chamberlain of the Royal Household and Senior Whip, a position he held until October 2013.

In October 2013 he was awarded a knighthood for political service.

In 2015 he was named a ‘Pub Champion’ by the British Beer & Pub Association for his campaigning to slash red tape and cut beer duty for pubs.

In 2015, he was a sponsor of the On-Shore Wind Turbine Subsidies (Abolition) Bill which prohibits of the use of public funds to subsidise ugly on-shore wind turbines, a measure which would bring to a halt the majority of new windfarm applications. The Bill was opposed by Labour.