I have found both my wife's and my bike will not allow me to go much over 16 MPH due to gearing, with my wife's she has 7 speeds on rear cog and already rather large jumps so to retain hill climbing ability very little can be done, and the from cog is domed to fit around the motor so can't really change it for multi-cog at front. It is possible my bike with a hub motor the gearing could be changed, but to be frank if going down hill I free wheel and up hill could not really exceed 16 MPH anyway.
The faster you go the more the prevailing wind has effect. I did live in Shotton near Chester, and there were two car free routes, one at side of river and one old railway route, and the wind tended to line up with tides, and it would reduce or increase my speed by 8 MPH on the river route, but not so much on rail route, but it resulted in time to get to Chester varied a lot due to wind, so to cycle to work you would need to allow for head wind.
However using wife’s electric bike in real terms if resulted in nearly the same time being tail wind or head wind, I was doing 16 MPH +/- 1 MPH what ever due to the legal limit on assistance. So I could say with some certainty how long it would take. So although with not speed regulation you may get 28 MPH with tail wind, likely 15 MPH with head wind so time to work still needs to be allowing for 15 MPH, so does not really help.
I find the hub motor in my bike not as easy to control to wife’s mid motor, and would have preferred a mid motor, but not really an option with a folding bike, however to alter the parameters with hears needs a PC and programming lead, mine I can problem from the controller, so can tell it I have a smaller wheel so it would go faster, although the speedometer would not show it as going faster. But still does not help as can’t pedal any faster anyway.
If it has a twist grip or thumb control it is only designed for walk assist, so that stops at 4 MPH so no real help. If it does not stop at 4 MPH not legal anyway, so does not really matter if you break other rules for e-bike, not an e-bike to start with.
I do question with my electric bike the 10th option, 0 = pedal assist only, 1 = twist grip control only, and 2 = both pedal assist and twist grip assistance, and it is reasonably easy to change, so could I suppose use on 0 with public roads and 2 with private, but so easy to change, so even on 0 not sure if legal, it is no different to selecting 0 to 5 for pedal assistance on main menu. So if without a key or tool you can change parameters is the bike legal? Is has a large CE marked on hub, but since even when in the EU rules changed country to country seems a bit odd.
However if your zipping along on the flat at 20 MPH and your feet are not turning it is rather clear that your bike is not an e-bike, as to registering as a motor bike or moped, not really an option as need a certificate of newness to register it. There should be a plate to show all the details, but even my wife’s e-bike from Halford’s has no plate, very clear does meet all requirements motor size and pedal assist top speed etc, but not strictly legal as no plate. Called the VIN plate on a car.
So if the police have a crack down, it really does not matter, most electric bikes are not technically e-bikes, I have looked for the old regulations in vain, I know when first came out you were allowed twist grip control only, and old bikes can still use twist grip or thumb controls for over 4 MPH, but can’t find date law changed, and again without the VIN plate how can one know the age of the bike? I remember talking to the owner of a scooter some years ago, and he showed me some paperwork saying how he was allowed on cycle tracks, clearly scooter format no options to pedal, but at that time legal.
So the 100 year old axe, it has had new heads, and had new stales, but still considered as 100 years old even though no single part is 100 years old.
But I would still keep the bike as legal as possible, and not pedalling up hill is a bit of a give away.