Earlier this week it was being reported that Streeting would launch his challenge today. However, there are still rumours suggesting he does not have the numbers to do so. He is a better communicator than Starmer, but it is not clear if he would be different in other ways. The soft left and left view him as continuity Starmer and don't want him. He is the least transfer friendly of all the likely candidates, so unlikely to win unless it is just him vs Starmer.
Burnham is the favoured candidate of many in the party, but he is not an MP so is not currently eligible to run. Yesterday, two seats were being floated as ones where the existing MP would be willing to stand down to allow Burnham to get back into parliament. One of the MPs involved has specifically denied that he would stand down for Burnham, and it is by no means certain that Burnham would win either seat if he did run. His naked ambition over the last few months has been an unedifying spectacle. He has run for the leadership twice before and proved to be a poor candidate on both occasions. His comments about the bond markets and suggestions from his supporters that the bond markets would have to fall in line with Burnham's agenda shows a detachment from reality. Governments fall into line with the bond markets, not the other way round. If the government wasn't so heavily in debt (£2.9 trillion and rising, the highest level relative to GDP since the 1960s) it may be able to ignore the bond markets, but that is not where we are.
The announcement that Rayner has cleared her issues with HMRC makes her a possible candidate. My view is that she would be a disaster as PM. Her history suggests a carelessness and lack of judgement which is not a good look for a PM. I don't think she has gravitas. And she has almost no track record in the economy, defence and foreign affairs, all of which are central issues at the moment. However, it isn't clear if she will run. She appears to support Burnham rather than wanting the job for herself, but if she runs she is the likely winner with the members, although it is not impossible that a Streeting vs Rayner vs Starmer contest could result in Starmer winning on second choices.
Milliband was being touted as the "stop Streeting" candidate a few days ago. However, with Rayner's tax issues apparently resolved, I doubt he will run.
At the moment, all the other possible candidates I have seen mentioned are either viewed as too strongly tied to the past or too low profile.
It is an interesting time in politics. Whether it is good for the country is another matter.