no, it won't be 144litres per min.
It might be 14, but measure it and see.
4ft head is not much.
It would be possible to double that by building a wooden platform in the loft reasonably easy.
The pipes from the tank to the cylinder, and the cylinder to the bath tap, should be 22mm diameter, as should the separate pipe from the tank to the bath cold tap (not 15mm which is the size of a finger). Look for any stopcocks or service valves on these pipes, which will restrict flow.
A good big 22mm pipe and a British tap will get plenty of flow even with a 4ft head. I was asking about the basin flow because if it is a pillar tap, not an imported mixer, it may be quite good.
if you do decide to get a new cylinder, get the biggest that will fit (they usually contain about 120 litres, which is enough for a good bath) and have the pipes replaced if they are not 22mm.
I am suspicious to hear the cold water has been restricted. This is often a bodge when a high-pressure cold supply is (wrongly) connected to the same mixer or shower as low-pressure hot.
As well as 22mm pipes, a UK-standard 3/4" Pillar Tap like this Bristan will give the best flow you can get. UK water supply is not the same as most European or US methods, so the plumbing and taps need to be different. Modern designs are also available if your taste differs from mine.