Acts of Parliment

An Act of Parliament may allow Ministers to make Regulations by Statutory Instrument. This is frequently done to fill in detail that might need to be changed frequently. For instance, the Income Tax (Earnings and Pensions) Act says "there will be PAYE", and empowers HMRC to make regulations that set out exactly how it works and what must be included on the various forms such as P45 and P60. 

Statutory Instruments also allow for the effects of inflation without having to take the increase all the way through Parliament. Land Registry fees are updated from time to time by Statutory Instrument. The original Severn Bridge Act fixed the tolls for crossing the bridge and over time it got ridiculously small. A new Act provides for the tolls to be increased by Statutory Instrument. 

Most major Acts include commencement provisions so that they do not come into effect immediately, only when the responsible Minister makes a Commencement Order by Statutory Instrument, usually when they're all prepared for it to start. The Marriage (Same Sex Couples) Act 2013 has been passed but is not in effect yet, to give time for register offices to prepare and get the new forms printed. When they're ready, the government will make a Commencement Order. 

The European Communities Act 1972 allows the government to bring EU Directives into force in the UK by Statutory Instrument, and that accounts for a lot of SIs. 

The Privy Council can also make delegated legislation using the Queen's powers under the Royal Prerogative, and these are Orders in Council. One example that comes to mind is if government departments are reshuffled, there will be an Order in Council to define the new departments. 

Finally, local councils and some companies have powers to make byelaws, usually regulating things like access to their premises. My local council has a comprehensive set for parks, regulating what you may and may not do in a park. Again they can do this because there are Acts of Parliament...