I will be attending a talk this weekend which will address the Muslim's role (if any) in politics. I'm assuming the talk will limit itself to British politics, but what I've written below applies to (secular) Muslim majority countries as well.
There are three aspects to answering this question:
Religiously, we need to asses the role of one's world view viz his/her interaction with society
The intellectual foundations of political activity of Muslims living in the West/East
What I call the 'Clash of the Paradigms', which deals with the religious movements' failure to provide practical solutions to society's needs.
I will touch on the first aspect in this post, the rest will follow after I've attended the event.
The Religious Aspect
Society plays a direct role in the spiritual development of a believer, since there are a number of existential perfections¹ that are unattainable unless one cooperates and interacts with others. An individuals' worldview is key to correct behaviour that will ensure those spiritual stations are achieved.
For the materialists, however, technological development and pursuing worldly pleasures is the only perfection, and his behaviour will reflect that accordingly. A religious person with a superficial faith in God, will have his eyes set on pleasures in the afterlife. He is motivated to adhere to religious laws, because he knows it's his key to enter paradise and avoid hell-fire².
True perfection, however, lies in attaining nearness to God. This worldview encourages the believer to search out and attain behaviours that will bring him nearness, and avoid everything that might create a barrier and veil between him and his Lord. Therefore, correct religious knowledge is essential to correct behaviour, in turn ensuring correct faith. As a person progresses in this path, he will realise that higher levels of perfection will require bigger sacrifices and harder struggles. Only those with strong resolve, patience and a true yearning for that closeness to God will ensure he evolves spiritually³.
The articles of faith ('aqeedah) are essential to shaping a person's world view and behaviours. A person who believes in the separation of religion and political activity, will not be motivated to pursue the establishment of social justice in this world. He has his eyes set on the afterlife, and will focus on the personal religious duties (to the minutest details) to ensure he avoids hell-fire. He will tell himself that it's the religious establishment's responsibility to sort out all his problems. Unfortunately, he would have most likely inherited this worldview from said religious establishment (his parents would ensure this reactionary vision is ingrained in his mind).
In order for us to contribute to society and interact at the socio-political levels, we will have to correct this superficial view of our faith, and move towards a deeper understanding of its concepts. The one-dimensional understanding of Islamic doctrines, where the emphasis is on juristic laws and personal religious duties (which have become rituals in most cases), is limiting us as individuals as well as communities in the diaspora. Ideologically, western concepts have taken over and dominated our thinking, where Islamic doctrines have failed to fill that gap, that yearning for a deeper understanding of the world. And once a person's worldview is confused with neo-liberal concepts, it becomes an uphill struggle to 1) change that worldview, and 2) for that person to live by an Islamic understanding of the world.
Even in Muslim majority countries, you will find this to be the dominant trend. Individual Muslims performing their obligatory religious duties, yet refrain from social contributions and cooperation, not due to any physical hindrances or lack of talents, but because their worldview is focused on 'material' gains in the afterlife!
In short, if we are serious about a revival of the stagnant state we are in, and are keen to contribute positively at the socio-political level (in the UK or elsewhere), we need to correct our worldview first, move away from legends, falls concepts and outright fabrications, and truly believe that with sincerity we can change the world ('O ye who believe! If ye help Allah, He will help you and will make your foothold firm' -47:7).
Once we, as a collective, appreciate that this isn't utopian fantasy talk, that our purpose is to evolve in the 'arc of ascent' towards perfection, we'll start to realise that this is only achievable if we characterise ourselves with the divine Names. Once this mindset is widely accepted, and becomes part of the collective subconscious, the idea of social justice will manifest itself naturally and organically, as each individual will have become a physical manifestation of the divine Name 'The Just'.
¹ I have spoken about this in detail in my other blog here.
² '..., and a group worshipped God out of desire for paradise, and that is the worship of tradesmen;...' - part of a narration by Imam Ali (as) in Nahjul Balaghah, Vol4, pg53 (Arabic edition)
³ Some people are willing to dedicate some of their time, usually at a personal level, however refrain from spending their money when the need arises. That is because his docility is limited, which in turn is due to the low goal he has set himself.