That was going to be my next question. Does the Police stop people with bikes that do not look like electric bikes all that much, such as the R&M Charger3(where the battery is integrated and the motor is also rather well hidden? Does the police know what to look for in general on these bikes?
They mostly don't bother with checking pedelecs, few officers knowing anything about them or their regulations. The exceptions are those forces who have trialled e-bikes for police patrol duties, plus traffic officers whose job it is.
Also if I limit the bike to be at normal pedelec speeds in town(which is sensible anyways) can I use the bike lane? Because if the regulation even attempts to be sensible it should allow for that...
If the rider can switch the bike into the faster mode, no, it's strictly illegal because it's a motor vehicle and no longer a bicycle. The definition that allows a pedelec to still be considered a bicycle and not a motor vehicle is not a regulation, it's an exemption from being subject to motor vehicle laws and it's very precise:
"pedal cycles with pedal assistance which are equipped with
an auxiliary electric motor having a maximum continuous
rated power of less than or equal to 250 W, where the
output of the motor is cut off when the cyclist stops
pedalling and is otherwise progressively reduced and
finally cut off before the vehicle speed reaches 25 km/h"
.