Is the coil in my hot water tank split?
If you are having strange pressure problems or the overflow is constantly running there is a small chance the coil in your hot water tank is split.
It’s important to check everything else before assuming it’s your hot water tank coil as it is very rare and very expensive to fix.
Follow the advice to try to narrow down the cause. If you have any doubts call a professional in.
Why is there a coil in my hot water cylinder?
The coil is just a long copper pipe bent into a coil inside the hot water cylinder. The water circulating in your radiators and boiler is filled with chemicals to reduce rust and sludge. This water (known as primary water) is pumped through the coil in the hot water cylinder and heats the water inside the cylinder (known as secondary water) without mixing with it.
In your attic or airing cupboard there will normally be two cisterns.
The large cistern feeds the clean secondary water into the hot water cylinder.
The smaller cistern feeds the dirty primary water into the boiler, radiators, and hot water cylinder coil.
If you have a pressurized system (there is a pressure gauge and a filling loop somewhere on your system) you will not have the small primary tank.

How do I know the coil in my hot water cylinder is split
It’s quite rare but the coil that holds the water from the boiler inside your hot water tank can split. If this is the case then either the lowest of the feed tanks will be overflowing or the boiler pressure will rise continuously.
To prove:
Tie the ball valve up in the bigger secondary tank so that no more water can enter the tank.
Run your hot taps so the level in the secondary tank is lower than the level of the smaller cistern. Don’t let the whole tank drain as that can cause airlocks in the hot water system.
As long as you don’t run any taps (sometimes the cold taps in the bathroom also come from this cistern) and with the ball valve still tied up the water level should stay the same.
If the coil is still intact and keeps the primary and secondary water separate the water levels will stay as they are.
If there is a leak in the coil the water levels of the two tanks should now equalize. The water level in the partially drained larger tank should slowly rise to the same level as the smaller primary tank.
As the split in the coil may be quite small it may take a while for the water level in the overflowing tank to go down, possibly several hours.
What should I do next?
The most effective solution to this problem is to replace the cylinder.
You can use central heating sealant chemicals to attempt to repair the pinhole in the coil. CT1 specifically says on their website that this is one of the uses of the miracle seal.
These chemicals have to first leak from the primary water into the secondary water. So for at least a short time, the sealant will be mixing with the hot water you will use for bathing. Personally, I would not recommend that but they know their product better than anyone.