Oh wait... isn't it the government who receives the payment for the fine? ;)
All this does is shift money. The government is just paying itself. It doesn't cost the taxpayer any more.
To some extent.
However, in the UK the police are funded partially through central government funds and partially through local council funds. People here pay income tax, which goes to central government, and a smaller amount of 'council' tax, which is for use on local services, police, fire departments etc.
What these fines do, in effect, is to take money that residents of the area have paid to police the local area and give it back to central government. The health service is currently fighting a similar £325,000 (over $500,000) fine.
These organisations should be held accountable for privacy breaches, but taking money away from residents and patients is not the answer.