I'll try to break the economy down in to the most basic method and why I feel cuts at this level, or more are required.
1. The level of gearing by the UK Government (i.e. how much debt we have) has resulted in interest payments which pushing us close to bankruptcy. If bankruptcy, or close to it, occurs our debt will get more expensive. It's a vicious cycle. This debt interest should be spent on services which would make our life better.
2. If the Government completely removed one sector of public sector jobs, all of those people would be unemployed. However the gap in the market for the services the Government used to provide would now become very enticing to private companies. These companies will require the same skills as these newly unemployed people have and the best of them will be recruited. If the public sector was inefficient, bloated or the service generally wasn't required, those people wouldn't be recruited again aka, the sector would become more efficient. If the private company fails to provide a decent service, another better company would appear and customers would use that new company. Competition occurs and both companies become more efficient, prices fall, services get better, salaries increase as skills improve. This competition currently won't exist in a public sector as there is no other companies to compete against. The higher salaried staff spend more of their money, resulting in jobs for those who didn't get reemployed.
With the private companies, rather than the staff costing tax payers money, the staff become tax payers and therefore positive contributors to the country. The Government can then do things like pay off its debt and put more money in to services which private companies would find difficult to provide. A perfect, but extreme example, is Hong Kong.
If the cuts aren't this deep, interest will remain too high. We still have to borrow more money each year and this will increase interest levels each year and will continue until good years where we can decrease the debt levels (something labour should have done, rather than spend more than income).