Thanks, that's much better.
A few points:
It looks to me like I can see limescale on the cylinder where it has cracked. This is bad news. You need a new one. If you start trying to unscrew the old immersion heater, or touch it much, the cylinder will probably come apart and a lot of water will gush out.
The heater looks pretty old, but that is not such a big deal, you can have a new one when the cylinder is changed.
It also looks like it has been leaking round the immersion as well, but that's no big deal as the rest of it is in such a poor state.
Sadly, a new cylinder will cost you in the region of £150*. It will be properly insulated so it will keep hot for at least 24 hours which will save you a pound or so each week in wasted heat. As you appear to have economy 7 or similar cheap-rate nighttime electricity, get the biggest one you can so you can have lots of half-price heat and not have to top it up during the day.
If there is any possibility that you will be getting a gas boiler in the next 20 years, get an indirect cylinder. It will cost little extra but can be heated by a boiler if you wish. Gas is much cheaper than electricity.
I think I can see a plastic waste pipe connected to the cylinder. this is very strange and not correct. I presume you have a cold water tank in the loft.
I would strongly advise that you ask around friends and neighbours for a local plumber that they recommend. He should be able to fit a new cylinder and immersion in half a day or so, without causing the floods and damage that might happen if you are not very good at plumbing.
Immersion heaters usually go into the top now, so you will want a long one. Get an Incalloy element which lasts a lot longer.
Some cylinders are available with a top heater and a bottom heater, but you probably won't need that.
I am not a plumber, just a fairly sensible housholder.
* edited: I should have said that is plus fitting, plus immersion, plus other parts