Replying to the OP.
The British Orthodox Church uses the Greek Liturgy of St James and the rites of the Coptic Orthodox Church for all other services and sacraments. I consider myself, as perhaps many here from different backgrounds and jurisdictions might do, as a Western Orthodox using an Eastern rite. We use only English, although I am always seeking to learn various pieces of liturgical text in other languages so that I can welcome those from other ethnicities. I consider myself to be entirely English and I worship as an Englishman.
But clearly I do not use a Catholic rite, and certainly not an Anglican one. As has been said, we venerate the saints of the British Isles, and take a great interest in our Christian heritage. I am organising an important conference next year in London on the Saints of the British Isles. It is natural for us to worship at the shrines of British saints. But Orthodoxy is wider than any one ethnicity, even the English, and in some sense I am sure that we wish to have a certain universality about our Orthodoxy so that we do not exclude others, while also being rooted in a real Tradition.
I have an interest in Francis of Assisi, Brother Lawrence, and in the Non-Jurors, and in the Little Gidding community. But I am interested in these secondarily and after a proper interest in the Orthodox Fathers of East and West, of the past and the present. I am interested, for instance, in the Eastern influences on Francis of Assisi, and on his relations with Eastern Christians when he was in Egypt. I think that he has been mich maligned and misrepresented by some Eastern Christians, but I am not and would not be an 'Orthodox Franciscan'.
I am also not much interested in many aspects of Anglicanism. I was never an Anglican. I was a Plymouth Brother. I therefore have no sense within me in which I see Anglicanism as on a continuity with Orthodoxy. There are of course those who were Anglicans in the British Orthodox Church, but the BOC is not a Continuing Anglican Church at all, and my own experience of Anglican enquirers is that they have tended to want to remain Anglican at any cost rather than becoming genuinely Orthodox. I don't believe it is possible to be Anglican and Orthodox. I don't believe that Anglicanism is Western Orthodoxy, and I don't believe that Orthodoxy should be, or needs to be, Anglican in some sense to attract English people. Most English people never visit an Anglican Church, and Orthodox worship in English is no more difficult to comprehend for such people than High Church Anglicanism.
The British Orthodox Church is not opposed to a Western Rite, but it is not appropriate for a small diocese to have multiple rites, and we find our liturgical unity in the Liturgy of St James. I have also to say that having used the same Liturgy for 17 years means that we have avoided all those heated discussions which seem to take place around the choice of a Western Rite.
So I will second some of the suggestions already made here. You would be more than welcome to attend a British Orthodox liturgy and I hope that you would find it interesting and spiritual, but it is the Liturgy of St James, it is not either the Sarum or Gregorian rite. If the rite is very important to you then there are groups in the Eastern Orthodox who are seeking to use forms of Western Rite. But apart from the issue of liturgical texts and practices, we are as committed to venerating and preserving our own local Christian heritage as much as anyone else. My own patron saint is buried just 18 miles from where I am sitting.
God bless your interest in Orthodoxy.