The only religion officially involved with politics in the UK is the Christian Church of England. Whilst the Queen is nominally the Supreme Governor of the Church of England, she appoints archbishops, bishops and deans of cathedrals on the advice of the Prime Minister.
Which is an interesting little detail when you consider that the two archbishops and 24 senior bishops sit in the House of Lords as the Lords Spiritual. That in itself has to bring into question the validity of the House of Lords as means to provide some form of checks and balances to what the House of Commons get up to (although in reality the Lords Spiritual only make up about 3% of lords in the house).
It also interesting when you then get pieces like this:
http://www.express.co.uk/news/uk/290460/David-Cameron-It-s-time-that-we-revived-Christian-values
So we have the PM encouraging us to adopt the values of a church of which he influences who should lead it. Convenient.
Should we remove the C of E from the political sphere? Well the media certainly seems to like to bang on about how the UK has become a secular place, so let's look at some numbers from the last two census (2001 & 2011):
2001
Christian 71.1%
Islam 3.1%
Hindhu 1.1%
Sikhism 0.7%
Judaism 0.5%
Buddhism 0.3%
No religion or not stated 22.3%
2011
Christian 59.4%
Islam 5.0%
Hindhu 1.5%
Sikhism 0.8%
Judaism 0.5%
Buddhism 0.8%
No religion or not stated 31.9%
So sure, there has been a significant reduction of Christianity but that's hardly a purely secular demographic. However we need to bear in mind that the 59.4% is not solely C of E Christians, there's a hefty proportion of Catholics, other Anglicans and all the other smaller denominations (that's a long list) - each of which have their own philosophies that vary from one another to a greater or lesser extent. On that basis there certainly does seem to be a case to remove any involvement of the C of E in politics as they no longer represent a majority of the population.
University College London published an summary paper on reforming the House of Lords and specifically the Bishops role within it back in 1999 that tackles some of the challenges around doing it and possible ways to go about it. It's an interesting if somewhat dry read and also covers briefly the history of how we came to this position in the first place:
http://www.ucl.ac.uk/spp/publications/unit-publications/41.pdf
So onto this question:
I don't know the answer, and I'm not clever enough to define new political directions, but isn't it time we made moves to remove religion from the democratic process?
That is actually an impossible thing to achieve. The majority of people (voters) in the UK have a religion and the majority of people who stand for election have a religion - so democracy being what it is religion will influence the process and arguably rightly so as a democratic government is meant to be representative of the population it governs. There is however a very good argument for removing the C of E influence in politics as its popularity is in decline.
At the end of the day, democracy is never going to be perfect, it was never intended to be - the idea is just to achieve governance that represents the views of most of the people most of the time. I'll take that over some of the possible alternatives like a totalitarian / dictatorial state (think Stalinist Soviet Union, Hitler's Germany or more recently Pol Pot's Cambodia) or an anarchy / no government (Western Sahara, Somalia anyone?).