You know what, religion is worthless if it stops you doing things you feel are important. Unless you truly believe that denying yourself something like love for something as petty as a difference of belief is a good and virtuous thing, then I honestly cannot understand how you can rationally say that you are going to allow your religion to prohibit you. If the OP honestly believed that his religion was a good enough reason to let this girl go, then he would not be in H&R, asking our advice.
Religion is about what *you* believe, not about what others tell you that you must believe. If your religion says "you must do X and Y", and you feel that Z is really important, then go and find a religion that fits how you truly feel and allows you to do Z.
I'm not naive, I know that in eastern countries there is an awful lot of tradition that must be considered, family honour etc etc. But just because it has been that way for hundreds of years does not make it right, good or even sensible.
And being born into a religion is NO excuse for not leaving it. I find it sickening that people actually put their families "need" to be viewed positively by the community before their own happiness. Who care if you will be seen as a traitor for leaving Islam? If you never chose it, what do you owe it? Since when did Islam have a monopoly on opinions? Yes, it is different in your native country, but in Britain, you can leave and never, ever look back.
I am not saying abandon your faith. I am simply saying that a bunch of rules and conditions for belief are worthless, because belief is a fluid, personal thing that no-one else can, or has a right to, control. Act as your conscience dictates, and do not be afraid to seek freedom from those who would control you.
OP, if she cares about you, she will allow her beliefs to accommodate you. It does not matter what her parents believe, it is what the two of you believe that matters. You are both free. I suggest you use that freedom.