Methods governments coud could use to discourage the use of private cars in the city centre [Si la audiencia es de ingleterra, la ortografía de esta palabra es correcta, pero si la audiencia es de los E.U., el ortografía es center.]

On the whole, governing bodies are entitled to wield influence over dwellers. their citizens. Accordingly, they governments must toe the party line and in turn, take care of their principles. observe ethical principles. Nonetheless, are they to restrict or constrain any determination, there could be any disapproval in accordance with citizen’s purposes. [This is unclear.  La palabra determination significa determinando, y mi pregunta es "¿determinando porqué?"]
Currently, it is working on diminishing the use of own privately-owned vehicles to enhance and provide usefulness.

For a start, people lack awareness of the encountered drawbacks of car exhaust fumes provoked   and are generally unwilling  to walk to work. Hence, Therefore, pursuing different educational approaches may slightly modify their reluctance. Thus, government could propose a motion diplomatically where everyone is able to cast their vote so as to make them learn the magnitude of the problem.

On the contrary other hand, population should be tiresome whether they were dictated to defray any fees. [Very confusing -- I cannot tell what you are trying to say.]Consequently, they would decline otherwise. Furthermore, they might feel thoughtless as the standard could be deemed a roundly deprivation of their timeliness to voice.
{Also very confusing.]

Personally, for the sake of both empathy and sympathy with people, the first choice could accomplish pedestrianizing the city swiftly. Seldom have people appreciated an extra share to pay, so little could the government achieve in that respect. Instruction wise, people seem to be more receptive when others take them into account.

Thank you so much in advance!! :)

Estimado Carlos,

En mi opinión, seria mejor si los párrafos fueron escritas mas sencillamente, lisa y  llanamente.  Claridad es el primer deber de la lengua, ¿sí?  

Buena suerte,

R.