What as the length of an immersion heater got to do with an open vented system, I think others have answered you above.
I will try an easy way for you:
make sure the water is turn off I suggest all the water to the house, cold water stop tap, run the hot water off a the downstairs tap, the lowest and when the water has stopped you should be able to remove the immersion heat ONLY IF IT IS IN THE TOP OF THE CYLINDER, you will need some old towels there will still be some water in the cylinder to the level of the heater connection.
Remove the heater and take it to your local shop and tell him you want one the same length.
Now, if by some chance someone has installed a short heater and the cylinder will take a longer one, its up to you.
Better still do you know a good local plumber, it will take him about 30 mins.