The Anglican 'blogger Pontifications has an article on the Filioque clause. Needless to say he writes from neither a Roman nor an Eastern Orthodox point of view, but the tone of his article suggests that the Filioque is something that Anglicanism is undecided on! I would have thought that as part of the Western theological tradition that the Filioque would be fairly well established in Anglicanism, but it's not something I've ever considered before.
Anyway, I might put together a proper post on the Filioque controversy myself at some stage, but due to lack of time cannot now. However, the following are some points which (to my mind) help justify the Filioque as a doctrine.
1. It is well established that the Latin word 'processio' (procession) is used to translate a Greek work which does not exactly have an identical meaning. The Greek word for procession implies procession from one point, the Latin 'processio' does not require this. Imagine a train which leaves Milan, goes to Florence and then to Rome. A Roman might say that this train proceeded from Milan and Florence. In Greek one could not say this - the train proceeded from Milan, but not Florence. Our hypothetical Roman and Greek have exactly the same understanding of what the train does and where the train goes, but for valid linguistic reasons the Greek cannot and should not say that it proceeds from Milan and Florence.
This difference of meaning was already well known by the time of St. Thomas Aquinas, and formed the basis for the abortive agreement between East and West at the Council of Florence.
2. It is possible therefore to talk of a shared understanding of the Trinity with much of the Eastern Orthodox world, even if there are linguistic reasons which impede its expression. However, there are some Eastern schools of Theology which will not even admit the above. They deny our ability to deduce the dual procession from the history of salvation. The West argues that from the life of Jesus Christ and the early church we see that the Holy Spirit is the spirit both of the Father and of the Son, and that both the Father and the Son are said to send it. Therefore, without denying the Father's role as font of divinity, the Holy Spirit can be said to proceed from both the Father and the Son. Some strands of the Eastern tradition do not allow this argument from the story of salvation back to the immanent relationships within the Trinity, but this quickly leads us to ask whether we are also impeded from deducing the Father-Son relationship within the Trinity from the life of Jesus Christ?
3. There are also theological arguments regarding whether without asserting the Filioque clause we make of the Holy Spirit a 'second son' and deny the uniqueness of the Father-Son relationship, but these are not conducive to brief presentation.