The Mountain and the Tree

Even the Romans admit that other churches exist, so it's not essential for a bishop to trace his lineage back to St Peter, as long as it goes back to one of the apostles. For instance, Coptic bishops trace their lineage back to St Mark. (For the avoidance of doubt, bishops tend to get ordained by several bishops all at once, often including one from another church, so in practice most bishops can probably trace their lineage back to all of the apostles.)

Unfortunately, the validity of Anglican orders is not as straightforward as you suggest. There's an extremely complicated controversy over it, which I'm afraid I can't possibly fit in a LiveJournal comment.