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In his time at Sport England, Draper had overall accountability for business turnover of £340m, and was involved in London’s 2012 Olympic bid, and the Wembley National Stadium construction project.
As Accounting Officer for Sport England, he had responsibility for reporting to Parliament through the Secretary of State for Culture, Media and Sport, and represented the organisation at a wide range of Select Committees, including the Public Accounts Committee hearing on the Wembley National Stadium Project, in 2003.
He also led a major review and reorganisation of the £450m spent on sport in the UK.
This included the completion of the £120m English Institute of Sport network of high performance facilities including new centres at Bath and Loughborough Universities, and a review of corporate governance across a number of sports, including athletics, hockey, rugby league, golf, cricket, boxing, karate and bowls.
Draper joined the LTA in 2006 and published the ‘Blueprint, a Strategy for British Tennis’, which set out his plans to transform the national governing body for British tennis. This included a complete restructure of the organisation, a new commercial strategy and programme, the introduction of Talent ID, and a comprehensive review and rebuild of all the LTA’s major events.
During his time at the LTA, turnover grew by 45% to £65m, and commercial revenues increased by three and a half times, in part the result of a ground-breaking Lead Partner agreement with pensions provider Aegon UK. British Tennis membership grew by 500% and the number of juniors playing competitive tennis sevenfold.
Draper was also responsible for introducing a new mini tennis programme and a nationwide talent ID system for British tennis. During this period, Great Britain won the Junior Davis Cup for the first time, and a number of British juniors won grand slam singles and doubles titles.   
In 2007 Draper withdrew funding from Naomi Broady, then age 17 and the leading junior, as a disciplinary measure for posting pictures and comments online wholly unrelated to tennis. This resulted in a feud which has resulted in Broady refusing to play for GB ever since and funding her own career. The general opinion of observers was that Draper was reflecting an LTA mindset which discredited tennis and put back attempts to widen participation beyond a narrow wealthy social group.
In 2013, Andy Murray became the first British man to win the Wimbledon singles title for 77 years.
The problems of participation came to a head when in December 2012 Sport England announced that £10.3million of the LTA's £17.4million funding total had been put on hold, with Sport England chief executive Jennie Price telling Press Association Sport: "Tennis has not performed well in terms of participation". Sport England subsequently released the funding to the LTA.
After his salary package at the LTA was revealed to be £640,000 in 2012, Draper and the LTA received further criticism, including from Baroness Billingham, the Chair of Parliament's All-Party Tennis Group.
Draper opposed the creation of the £40 million National Tennis Centre at Roehampton, and in August 2014, it was reported that the centre was to close, just 7 years after it was opened. 
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