On Theo's point: obviously it would be better, more productive, if we could unite the various factions into a single organisation with a democratic regime allowing debate and dissent.
The nearest we've come towards that in living memory was the Socialist Alliance of around 2001. But... the SP was never really "in" it, just observing. (For example, they played no part in the quite lively SA conference which debated the SA's 2001 election manifesto, just sending a small delegation which sat stony-faced at the back of the hall). Then they got out as fast as they could, in late 2001.
The SWP stuck with it a little longer but then decided to go for an alliance with George Galloway instead of with the rest of the left.
We (AWL) and others tried to keep the SA going, but weren't strong enough. (In fact, Pete McLaren and a few others still keep the name "SA" going, but I fear with little content now).
AWL launched a call for a new Socialist Alliance in 2009 at the time of the big UKIP and BNP electoral successes. Both SWP and SP were talking about forms of left unity at the time, but both made it very clear that they wanted unity with high-ranking union officials rather than other left groups.
From their own angle, I guess that was a rational response: as Taaffe's stuff on Libya shows, they do have more in common with some scoundrelly "left" union officials (who have Stalinoid right-wing views on world politics) than with revolutionary Marxism. The SP also has more in common "socially" with left-wing union bureaucrats, since in the unions the SP are, functionally, "the political wing" of the PCS bureaucracy, subordinated to it in the same way that the "political wing" was subordinated to the "military wing" in traditional Irish Republicanism. That might change, but it is the way things are now.
What now? We can't afford to wait, doing nothing, until the SWP and SP either think differently or become reduced over time to dimensions where their opposition to left unity is inconsequential. We have to build the best revolutionary socialist organisation we can, both to take forward the struggle now and to create the agency for welding future broader unity.