Removing electric bath and central heating system

[Puolukka]

We are about to move into a house with electric bath and gravity fed central heating system (old boiler + hot water tank in the bedroom + cold water tank in the loft). We are going to redo the bathroom and want to get rid of the electric bath and replace it with boiler-based system.
What are possible approaches?
Given that I want to have good water pressure for shower and don't want to add a noisy pump, can I use the current system?
Or do I need to upgrade it to a combi boiler or unvented system? What are the approximate cost of each? We are in Middlesex, England.
Thank you, all!

What is an electric bath?

What colour is the hot-water cylinder?

Is there a gas boiler?

How old is the house?

I am sorry for a typo. That is an electrical shower. The house was built in 1950 with gas boiler. The colour of the hot water cylinder looks like bronze. Thank you!

You can keep the electric shower if you want. If you can afford it, an unvented cylinder will give you the best service and will give an unsurpassed shower. Your old cylinder is very old, probably original, and overdue for replacement.

Your incoming water supply is probably half inch and would benefit from being replaced with 32mm plastic all the way to the pavement. This will involve digging a trench and fitting bigger stopcocks. Ask the plumber to test the flow and tell you what it is before quoting. 20 litres per minute would be good.

If the flow is not enough for an unvented, it will give poor performance with a combi. A modern combi should give 12 litres per minute of hot water, and you do not want this to reduce when somebody turns on a cold tap or flushes a WC.

If the gas boiler is a good one and still working you do not need to replace it yet. If it is old you may need to find an independent local gasman familiar with the type.

The new cylinder can go anywhere but please don't put anything in the loft.

If you buy a new boiler put it close to an indoor drain, such as the kitchen sink, to avoid outdoor pipework.

This is very kind of you! Thank you!