Sorry SS but the flow is so low ( about 4.6 litres/minute cold) (from 60/13 seconds) that the pressure drop in the PIPE is going to be pretty insignificant.
The shower valve is clearly adding a lot more resistance than your bath taps where both flows were about 12 litres/minute.
It's like you have a fixed voltage ( the head of water) and lousy current(flow).
So you have a big resistor in there. You work out the resistance from Ohms law and it says there's say 50 ohms ( like 50 metres of pipe!). So removing the resistance of a couple of metres of pipe, like removing a couple of Ohms, is not going to make a significant difference. You'll still have 48 Ohms.
If the flow was lowish but the resistance worked out to a total of 6 Ohms , then removing 2 Ohms would make a big difference.
I worked it out best I could for the bath, and it wasn't much, so it's going to be less for the shower.
It's like having a high resistance light bulb designed for 240V and using it on 110 volts. Making the cable fatter won't make the difference. I'm labouring this, sorry!
Your shower could be something like the one my father used as above, you have similar flow.
Your HOT flow
will be a lot lower than your COLD flow
if the water's cold - the mixer (assuming it's thermostatic) will try to stop the water - cos it's cold!
So when you have
hot hot water you should get something like 4+ liters a minute from each side, eg 4.6 from the hot and whatever from the cold to get the temperature right, which will be about 7 litres/minute. Well you won't smell anyway.
But the speed of the water at the showerhead will still be poor. You'll get a
wash from a gravity shower but nothing exciting.
He thinks this will reduce the pressure.
Increasing the pipe size - he doesn't understand much, does he. He probably has it in his head that the water will go slower (speed) through the bigger pipe, which it will. Irrelevant to you. Nothing to do with pressure at the head.
If you're confused as hell now, consider the Electric shower.
They HAVE to reduce the flow to about 4l/min because otherwise the 11kW or whatever, can't heat it up enough. They do that by making the holes in the showerhead small. The actual pressure is mains, which is HIGH. So all the pressure is dropped across the resistance of the holes in the head. Because the pressure's there. The water is forced through at high speed. So it hits your back at high speed and feels like a half decent shower.
YOU can't use a head like that with your 4l/min, because your pressure's low, so it'll be a dribble at 4l/min instead of fine jets at 4l/min.
Your plumber should have worked all this out
before he started. If he didn't know how, he should have found out.
Yes he should have fitted 22mm from the off, but he should have known it wouldn't give you great flow anyway.
If you push a shower/tap/valve manufacturer, you CAN get figures, eg if you ask then what flow you will get when the pressure is (say) 0.2 bar, they DO have the graphs to look at. Getting someone who understands, can be ridiculously difficult though. I've just looked for data online for 3 makes and found squat.
SO your options... Apart from the pump, you could look for an even lower operating pressure shower, but the lowest I've seen says 0.2 bar, and that's all you have, so don't expect much. (No they
don't quote resistance or flow!). No mileage there then.
What about lifting the tank in the loft?
The ACTUAL head you have while you're showering is from the water level in the cistern to the shower head.
I bet that's less than 2 metres.
8 ft ceiling, head 1ft 6 from the ceiling, plus the joists and boards, plus water depth say a foot, that's about ONE metre.
( sorry I'm old, I swap between units...)
So if you could lift your cistern by a metre, you'd double your head. Lots of people do it with 4x2s and ply, it works. Use plastic 22mm if you like, it doesn't take all that long.
You would
somewhere near double your flow.
14l/min shower is plenty good enough.
Sorry you're gonna have grief from your "plumber" . Tell him your wife has stopped washing your socks and is threatening to stop feeding you. At least then you'll get a bit of sympathy. Someone as thick as him must have had trouble with his wife at some point in his life.
Good luck!
