If you are thinking of upgrading your old central heating system then you wouldn’t go far wrong with a system that includes a system boiler alongside a high efficient unvented cylinder.
Upgrading your cylinder will certainly help with the bills. In the old days the copper cylinder in the airing cupboard would lose most of its heat as it was not insulated! New Cylinders are cold to the touch which means they are far more efficient. The more heat that the cylinder retains means that the next time you want hot water it is more likely that the energy required to get it back to temperature will be vastly reduced. The new cylinders also have high recovery coils that reheat the cylinders within 20 minutes.
The choice of cylinders these days might leave you with a headache but the main difference is that some makes such as Ariston are made from Standard Steel and therefore have only a 10 Year warranty whereas makes such as Oso or Range are made from Stainless Steel and carry a 25 year warranty.
You can find out how to size your cylinder here