What are you Brits going to do when the Muslims form their own political party as they did in the Netherlands? You gonna kiss up and bend over for them because that is what they expect and with so many faithful Islamics who seem to thrive there it won't be long. In Europe the Churches are empty on Sunday but the Mosques are FULL on Friday. Good luck to you because you will need it.
The Respect Unity Coalition is currently the nearest we have to a political party for Muslims. It is a very minor party. It grew out of the anti-war movement. I would be happy to see more power for a party whose stated policies include "Opposition to all forms of discrimination based on race, gender, ethnicity, religious beliefs (or lack of them), sexual orientation, disabilities, national origin or citizenship. The right to self-determination of every individual in relation to their religious (or non-religious) beliefs, as well as sexual choices."
Where I live, the churches are full on a Sunday. Thanks for your concern.
What other political parties have major influence in the UK?
The Labour Party is in government, that's a fairly major influence. The Liberal Democrats have always been the third party behind the Conservatives and Labour, but as Labour's policies become indistinguishable from Tory policies, and the Conservatives make themselves look sillier and sillier with endless internal wrangling and leadership disputes, the Lib Dems are moving into second place behind Labour.
There are dozens of other political parties: Plaid Cymru, Ulster Unionist, Sinn Fein, Scottish National Party, some of whom have seats in parliament, some of whom have seats on National Assemblies or the European Parliament.
More info here:
http://news.bbc.co.uk/1/hi/uk_politics/political_links/81344.stm