The public sector is huge!  At the last count it constituted approximately:

434 local authorities

22 government departments

450 NHS trusts

43 police services

45 fire and rescue services

334 universities

3500 secondary schools

24000 primary schools

numerous departments, agencies, bodies

etc etc etc

All these bodies have to purchase the goods and services they require in accordance with procurement legislation.

There are many other publicly-funded bodies which also have to adhere to this legislation that you might be unaware of and haven’t previously considered as a potential client. 

For example:

Driving Standards Agency 
Transport for London
The British Library
British Nuclear Fuels
BBC
Crown Agents
 

And don’t forget all the museums, galleries, archives, Regional Development Agencies - the list goes on and on.