Remove water tanks and fit instantaneous water heaters?

[Halitosis]

Hi all. Got a leaking hot water tank (around the immersion element) and wondering what is best for the long term. It's 30 years old (very soft water area!) in a one bedroom flat with no gas and an electric shower (no bathtub either) so the large hot water tank and similarly large header tank above it in the hallway closet only serve the 2 sinks (kitchen and bathroom).
So what's recommended: repair, replace with a like-for-like cylinder, a pressurised system (electric), or is it possible to remove it all and instead have one of those electric instantaneous water heaters under each sink?
Presumably the cold water taps usually/already run direct from the mains supply rather than the header tank?), and these could be some sort of mixer tap so use the existing cold supply pipe?
As you can tell, I'm largely clueless with plumbing! Thanks for any advice

 

[flameport]

If possible, an 80 litre unvented cylinder with a 3kW immersion heater in it.
You can then get rid of the electric shower. Cylinder will supply all of the outlets at mains pressure.

 

[Halitosis]

Update: had a good plumber in who recommended a like-for-like replacement. although a pressurised system would be an upgrade, given it only supplies the kitchen and bathroom sinks it really wouldn't be worth the effort or cost. Similarly an instant hot water heater would do away with the cylinder (and header tank), but the consumer unit is across the flat and running the necessary cable would be a faff.
So a new (smaller and more thermally efficient) cylinder with a 3kw immersion heater is going in soon.
Cheers