"How does a British girl from a liberal family decide to become Muslim?"
I always knew that God existed, despite being told otherwise, but didn't really have the opportunity to explore this belief. I buried it for a long time, and lived with a feeling of unspecific discontent until my mid 20's. At this point I would say that my life was shallow, I was an arrogant person, I had built an identity for myself based on meaningless things. I had no limits in my life, other than 'don't hurt anyone', but as is inevitable with a morality based on flawed human intellect I hurt others and myself. In the language of the Quran, I wronged my own soul.
Through a shared interest which was unrelated to religion I met a Muslim family who I became very friendly with. They were practising Sufi-ish Muslims, and I was fascinated by them, and also really admired their dignity. It didn't take long before I started asking questions, and then ensued a period of time filled with lots of late night soul searching conversations. This was the first time in my entire life that I was having conversations which were actually reaching the depths that I had inside me, and it was an amazing time.
These people were immensely helpful (and still are) but very hesitant not to be pushy, and I went further afield to find out more information (I was also a bit embarrassed to tell them how interested I really was). Eventually someone gave me a Quran. I read it from cover to cover. At first I found it really harsh, I had never read the bible or any other religious book. But then this happened:
"Allah has sent down the best statement: a consistent Book wherein is reiteration. The skins shiver therefrom of those who fear their Lord; then their skins and their hearts relax at the remembrance of Allah . That is the guidance of Allah by which He guides whom He wills". (Quran 39:23)
I had to research a lot of issues I had misconceptions about before I could accept Islam and agree to live by its' rules. But having done the 'liberal' experiment I could certainly accept that their needed to be rules.
"I find it very difficult to understand how British women born to liberal families give up all those liberties, cover up head to toe, accept to be segregated from men, and have arranged marriages with some guy just because he is Muslim"
As I said, it was easy to give up liberties that I realised got me nowhere, but I should make it clear that as a Muslim woman I have worked, studied, played a role within the Muslim community, been outspoken about important issues, and have received far more respect from Muslim men than I ever did from non-Muslim men.
Covering head to toe I always found easy, I see it as a sign of dignity, not oppression.
Muslims vary in the amount of segregation they require. I rarely socialise with men, apart from an exceptional couple of families where we might all eat a meal together, and I am happy with this. But at work, in organising events for Muslims, in general life I have contact with men. Muslim women all over the world have contact with men all the time, which is fine so long as etiquette is observed.
I didn't have an arranged marriage (most converts don't as it's normally parents who arrange a marriage). My husband asked me to marry him and I said yes, completely of my own free will. And I also didn't marry him just because he was Muslim, although that was definately a necessity!
Hope this long reply answers your question Cote!