Contrary to common assumption, the United Nations does not maintain an office in London. The UN's primary headquarters is in New York City, USA, on international territory along the East River in Manhattan.
Headquarters: New York City (Secretariat, General Assembly, Security Council, ECOSOC)
Major Offices: Geneva (Switzerland), Vienna (Austria), Nairobi (Kenya)
Regional Commissions: Addis Ababa (Africa), Bangkok (Asia-Pacific), Beirut (Western Asia), Santiago (Latin America), Geneva (Europe)
The UK hosts several UN-related entities, but not a UN headquarters office:
The UN's location was fixed in 1945-46. The US offered the NYC site (Rockefeller donation); London was wartime-damaged and declining as imperial capital. The specialized agencies distributed globally reflect functional needs (IMO: maritime; ICAO: aviation in Montreal; WIPO: IP in Geneva).
For UN matters from the UK: contact the relevant agency directly or the UK Mission to the UN in New York. The UN Information Centre for the UK is actually in Brussels.