Many British organizations use choice voting (called the single transferable vote in the United Kingdom) for their elections. Here is a partial list, as of June 2008 -- note that there is a slight chance that some of these organizations either use a different ranked ballot system or have changed their election method recently.

Organizations:

3M  
AA  
Abbey National Group Union  
Amnesty International ASLEF Association for Physical Education  
Association of Anaesthetists of Great Britain and Ireland   
Association of British Clinical Diabetologists       
Association of Paediatric Anaesthetists     
BAA 
Barnsley Hospital NHS Foundation Trust      
Basildon & Thurrock University Hospitals    
BECTU BFAWU Birmingham & Solihull Mental Health NHS Trust Blackpool, Fylde & Wyre Hospitals NHS Trust 
BMA - GPC   
BMA Consultants Committee   
BMA Council 
BMA Junior Doctors Committee BMA Medical Students Committee      
BMA Science & Education     
BMA Scotland Bolton, Salford & Trafford Mental Health Trust      
Bradford Teaching Hospitals NHS Foundation Trust    
BRIT Awards Ltd     
British Airways Pensions    
British Computer Society    
British Humanist Association British Medical Journal     
British Transplant Society  
Cemex Centrica plc Chartered Institute of Linguists    
Chartered Society of Physiotherapy  
Chelsea & Westminster NHS Trust     
CIMA Clatterbridge Centre for Oncology NHS Foundation Trust      
Community   
Conservative Party  
Countess of Chester Hospital NHS Foundation Trust   
Crewe and Nantwich Borough Council  
Crown Estate CSC 
Derby Hospitals NHS Foundation Trust East London & The City Mental Health NHS Trust      
EDF Energy  
Educational Institute of Scotland   
Electoral Reform Society    
Ernst & Young Eversheds   
Family Law Bar Association  
First ScotRail      
First TransPennine Express  
FSA 
Fujitsu     
Gallions Housing Association General Council of the Bar  
General Teaching Council for England General Teaching Council Wales      
Gloucestershire Hospitals NHS Foundation Trust      
GMB 
Goitre Tower Anthracite Ltd 
Harrogate and District NHS Foundation Trust 
HAVCO (Haringey Association of Voluntary and Community Organisations)
Higher Education Academy    
Homerton University Hospital NHS Trust      
HSBC IBM United Kingdom Pensions Trust Limited   
IET 
Institute of Mechanical Engineers (IMechE)  
Institution of Civil Engineers (ICE) IOSH Kings Fund  
International Continence Society
Lancashire Care NHS Foundation Trust Lancashire Care NHS Trust   
Lancashire Teaching Hospital Foundation Trust Law Society 
Liberal Democrats   
Liberty     
Liverpool Women's NHS Foundation Trust      
London Civic Forum  
London Metropolitan University      
Londonwide Local Medical Committee  
Mensa International 
Mid Cheshire Hospitals NHS Trust    
Milk Link Limited   
MS Society  
MS Society Scotland 
National Autistic Society   
National Grid National Housing Federation 
National Union of Teachers  
NCVO - National Council for Voluntary Organisations 
New Cross Gate NDC  
NISA Norfolk and Norwich University Hospital NHS Trust   
North Essex Partnership NHS Foundation Trust (prospective)  
North Lincolnshire and Goole Hospitals NHS Foundation Trust 
Northamptonshire Healthcare NHS Trust Northern Bank Pension Trust Limited
Northern Circuit
Northern Ireland Water      
NORTHUMBRIA HEALTHCARE NHS FOUNDATION TRUST 
NUJ - NEC   
NUT 
OASIS (Organization for the Advancement of Structured Information Standards)
Octavia Housing & Care      
Open University     
Oxleas NHS Foundation Trust 
Papworth Hospital NHS Foundation Trust      
Partnership of East London Co-operatives (PELC) Limited     
Pensions Management Institute Pensions Trust      
Pensions Trust, The 
Peterborough and Stamford NHS Foundation Trust      
Portsmouth Hospitals NHS Trust      
Princess Royal Trust for Carers, The PwC 
PwC Hong Kong Rail Safety & Standards Board
RAISE
Reading University Students' Union  
RIBA RMT 
Royal Academy of Engineering Royal Bolton Hospitals NHS Trust    
Royal Bournemouth and Christchurch Hospitals NHS Foundation Trust   
Royal British Legion Royal College of General Practitioners       
Royal College of Midwives   
Royal College of Nursing    
Royal College of Paediatrics and Child Health Royal College of Physicians 
Royal College of Psychiatrists       
Royal College of Surgeons   
Royal Free Hampstead NHS Trust      
Royal Town Planning Institute Sanofi Aventis      
Scottish Federation of Housing Associations 
Scottish Tobacco Control Alliance   
Senior Council for Devon    
SFLA (Solicitors Family Law Association)    
Sheffield Teaching Hospitals Shell Pensions Trust Ltd    
Society for Cardiothoracic Surgeons of Great Britain & Ireland      
Society of Operations Engineers     
South Essex Partnership NHS Trust   
South Staffordshire Healthcare FT   
Stockport NHS Foundation Trust      
T & G Taunton and Somerset NHS Trust      
Telegraph Media Group
Terence Higgins Trust
The Headmasters' and Headmistresses' Conference     
The Rotherham NHS Foundation Trust  
Theatrical Management Association   
Turkish/British Chamber of Commerce 
UCATT UCLH NHS Foundation Trust   
UCU (University and College Union)  
UK Athletics UK Athletics Ltd    
UNISON      
Universities Personnel Association  
University & College Union - Open University Branch 
University of Birmingham    
University of Central Lancashire    
University of London Union  
University of the Arts London
Vegan Society
Whitehead Mann LLP 
Wirral Hospital NHS Trust  

See a list of U.S. organizations that use STV

See where IRV has been adopted