Question: What United Kingdom government is based in "The Doughnut" in the suburbs of Cheltenham and works alongside MI5 as part of the United Kingdom's intelligence machinery?

Context paragraphs:
Directorate-General for External Security: The General Directorate for External Security (French: "Direction générale de la sécurité extérieure" , DGSE) is France's external intelligence agency.  The French equivalent to the United Kingdom's MI6 and the United States' CIA, the DGSE operates under the direction of the French Ministry of Defence and works alongside its domestic counterpart, the DGSI (General Directorate for Internal Security), in providing intelligence and safeguarding national security, notably by performing paramilitary and counterintelligence operations abroad.  As with most other intelligence agencies, details of its operations and organization are not made public.

Government Communications Headquarters: The Government Communications Headquarters (GCHQ) is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance to the government and armed forces of the United Kingdom.  Based in "The Doughnut" in the suburbs of Cheltenham, GCHQ is the responsibility of the country's Secretary of State for Foreign and Commonwealth Affairs, but it is not a part of the Foreign Office and its director ranks as a Permanent Secretary.

United Kingdom government austerity programme: The United Kingdom government austerity programme is a fiscal policy undertaken in response to the Great Recession.  It is a deficit reduction programme consisting of sustained reductions in public spending and tax rises, intended to reduce the government budget deficit and the welfare state in the United Kingdom.  The National Health Service and education have been "ringfenced" and protected from direct spending cuts.  United Kingdom austerity policies have received pointed criticism from left-wing politicians and economists, and have prompted anti-austerity movements among citizens more generally.

Edinburgh Agreement (2012): The Edinburgh Agreement (full title: "Agreement between the United Kingdom Government and the Scottish Government on a referendum on independence for Scotland") is the agreement between the Scottish Government and the United Kingdom Government, signed on 15 October 2012 at St Andrew's House, Edinburgh, on the terms for the Scottish independence referendum, 2014.

Department for International Trade: The Department for International Trade (DIT) is a United Kingdom government department responsible for striking and extending trade agreements between the United Kingdom and non EU states (however the UK Government is not legally permitted to negotiate any trade deals with third party countries before it has exited the EU).  The department was created by Prime Minister Theresa May, shortly after she took office on 13 July 2016, following the United Kingdom's vote to leave the European Union.

Intelligence and Security Committee of Parliament: The Intelligence and Security Committee of Parliament is a committee of Parliament of the United Kingdom appointed to oversee the work of the intelligence machinery of the United Kingdom.

The Doughnut: "The Doughnut" is the nickname given to the headquarters of the Government Communications Headquarters (GCHQ), a British cryptography and intelligence agency.  It is located on a 176 acre site in Benhall, in the suburbs of Cheltenham, Gloucestershire, in South West England.  The Doughnut houses 5,500 employees; GCHQ is the largest single employer in Gloucestershire.  Built to modernise and consolidate GCHQ's multiple buildings in Cheltenham, The Doughnut was completed in 2003, and GCHQ moved into the building in 2004.  It is the largest building constructed for secret intelligence operations outside the United States.  The Doughnut was too small for the number of staff at its completion, and a second building in a secret and undisclosed location in the 'Gloucestershire area' now also accommodates staff from GCHQ.  The Doughnut is surrounded by car and bicycle parking in concentric rings, and well protected by security.

MI5: The Security Service, also MI5 (Military Intelligence, Section 5), is the United Kingdom's domestic counter-intelligence and security agency and is part of its intelligence machinery alongside the Secret Intelligence Service (MI6), Government Communications Headquarters (GCHQ) and Defence Intelligence (DI).  MI5 is directed by the Joint Intelligence Committee (JIC), and the service is bound by the Security Service Act 1989.  The service is directed to protect British parliamentary democracy and economic interests, and counter terrorism and espionage within the UK.

British intelligence agencies: The Government of the United Kingdom maintains intelligence agencies within several different government departments.  The agencies are responsible for collecting and producing foreign and domestic intelligence, providing military intelligence, performing espionage and counter-espionage.  Their intelligence assessments contribute to the conduct of the foreign relations of the United Kingdom, maintaining the national security of the United Kingdom, military planning and law enforcement in the United Kingdom.  The three main agencies are the Secret Intelligence Service (MI6), the Security Service (MI5), and the Government Communications Headquarters (GCHQ).

Executive agency: An executive agency is a part of a government department that is treated as managerially and budgetarily separate, to carry-out some part of the executive functions of the United Kingdom government, Scottish Government, Welsh Government or Northern Ireland Executive.  Executive agencies are "machinery of government" devices distinct both from non-ministerial government departments and non-departmental public bodies (or "quangos"), each of which enjoy a real legal and constitutional separation from ministerial control.  The model was also applied in several other countries.

Supporting paragraphs: MI5 Government Communications Headquarters
Answer: Government Communications Headquarters