Well this is very interesting!! In our religion, having any type of boyfriend/girlfriend relationship before marriage is not allowed, and things like touching, kissing, premarital sex etc are really not allowed!! This is because men and women are supposed to respectfully approach each other for marriage and have commitment on both sides (ie marriage) before this.
So not sure how to help you exactly. It sounds like she may be not so practicing. (The smoking though I have to say some Muslim scholars allow, but it is disliked-- for men or women.)
Honestly, it sounds like you would like to make the relationship more than what it is and would like to know more about her and her religion so maybe it would be good to talk to her about it. She can teach you more things about Islam and Muslims and I'm sure the Mosque would be fine with you visiting and talking to the people there! You definitely wouldn't offend anyone by going!! Most Mosques are pretty welcoming here in the US, I'd assume the same for the UK! (I've heard good things about the East London Mosque and the Regents Park Mosque.)
I just also want to add that maybe she just wants to try something "forbidden" and doesn't want to do anything more than that! In that case, it would be good for you to know so your feelings don't get hurt. She may also really like you but doesn't think you'd be interested in taking the relationship to a higher level by getting to know her religion and family etc. So definitely talk to her and see what happens!
Hope everything goes well,
Ok take care!!