I came over six years ago, and after about two, I knew I was never going back. It does help that I'm in London - in the countryside people always seem taken aback by my accent.
I do feel at home here, and I guess it helped that after a year I acquired a British boyfriend. :) My circle of friends are all Brits or international types; I don't socialise with people from my home country: I'm very much on the left and a feminist, and my home country is quite traditional and patriarchal. Hence me living here.
I adore London, and I feel completely integrated. I work, go to uni, volunteer for a mental health charity in my neighbourhood. I can't imagine ever going back. I plan to get my British citizenship, though I consider myself a 'citizen of nowhere'.
A practical advice: volunteering even a couple hours per week could be a nice way to connect with locals. Also adjusting your expectations: according to many we will always be foreigners here, but that's not your problem, it's theirs. :) I'm a Londoner, and I'll fight anyone who tries to insist that I don't belong. :p
Give yourself time - you need experience and practice to really learn the ins and outs of British life. Listen to the radio, watch TV shows, read English books and magazines. All that will help you to get acquainted with British culture. All the best. Don't despair. Xx