It is fairly obvious that hot water pipes and hot water storage cylinders should be insulated to prevent heat loss. Newer cylinders already have insulation pre fitted, but if your tank is older and un-insulated then according to the Energy Savings Trust by fitting a hot water jacket you will save about £ 40 per year. Your savings would be even more however if you regularly use an electrical immersion heater, since it costs a lot more to heat water with electricity.
Given that a new thick jacket (75mm) for a hot water tank costs about £ 12, it should pay for itself in less than six months. Even upgrading and old thinner jacket, is worth considering and will pay back the investment in about 2 years.
This energy/money saving measure is almost a must do. Even if you are renting off a landlord who is too tight fisted to put a jacket on the cylinder, you could buy one and take it with you when you leave!
Insulating hot water pipes will save you less, possibly £ 10 per year but DIY installation is very easy and materials will only cost about £ 10. So it will only take a year to payback this investment.
