New emails released from Hillary Clinton’s private server show David Miliband confided in the then secretary of state that losing the Labour leadership election was “tough” and having won the support of the party members and MPs made it “doubly so”, adding ruefully: “When it’s your brother…”.

The former UK foreign secretary – who enjoyed a famously close working relationship with Clinton while in office – thanked her for a “poignant” message (which was not one of those published) after he lost the battle to lead the party to his younger brother, Ed, in 2010.

The email, published in the latest batch of correspondence released from Clinton’s private server on Monday night, came from an address beginning “D.Gunners” – Miliband is an Arsenal fan.

Although any reply from Clinton does not appear in this round of emails, the cache does show her response to news from an aide that Ed Miliband had won. “Clearly more about Tony that[sic] David or Ed,” Clinton wrote to Sidney Blumenthal, a long-time adviser.

An email to Clinton from her aide, Huma Abedin, entitled “Ed Miliband is new UK Labour party leader” contained a one-word message: “Wow.”

David Miliband emails Clinton after losing race to be Labour leader. His email is "D.Gunners" pic.twitter.com/Ttu65Cu0Rl — Ben Jacobs (@Bencjacobs) September 1, 2015

The wider cache of emails reveal an apparent fascination with Labour infighting as the 2010 general election loomed, with Blumenthal sending frequent updates to Clinton on Gordon Brown’s rumoured reshuffles, the resignation of minister James Purnell, and Labour’s poor showing in the 2009 European elections.

Many of the missives centred on David Miliband’s prospects, with Peter Mandelson a much criticised figure in emails from Blumenthal. Several emails relay apparent attempts by Mandelson to ease Miliband out of his role as foreign secretary, with one update on a rumoured demotion post-European elections eliciting a response from Clinton: “Very sorry to read this confirmation.”

In another message subtitled “Mandelson Watch”, the adviser writes that the then business secretary had manoeuvred to have Miliband moved to the EU foreign minister role in order to secure the UK foreign office for himself.

Thwarted, Mandelson “tried to seize the EU position for himself”, Blumenthal writes. “The Europeans thought him mad. Suddenly they recalled his bad or strange behaviour as UK commissioner to the EU.”

Blumenthal was apparently not keen to see anyone else in the foreign secretary’s chair either. In an email sent in the messy aftermath of the 2010 general election in the UK, he wrote to Clinton: “I would doubt you’ll see David again as foreign secretary. Prepare for hauge [sic, William Hague], who is deeply anti-European and will be disingenuous with you.”

Before the election, Blumenthal also wrote scathingly of Conservative leader David Cameron, telling the secretary of state: “Cameron would be superficially friendly and privately scornful. Class has a lot to do with the contempt. A Cameron government would be more aristocratic and even narrowly Etonian than any Conservative government in recent history.”

In response to the long rundown of the machinations behind the 2010 coalition talks, Clinton responded to Blumenthal: “I shared your emails w Bill who thought they were ‘brilliant’! Keep ‘em coming when you can.”

Hillary Clinton had earlier written that she had had drinks with Miliband ahead of the election: “I have crossed fingers!”

In an interview with Vogue magazine in 2009, Clinton told an interviewer who had complimented Miliband’s accent: “If you saw him it would be a big crush. I mean, he is so vibrant, vital, attractive, smart. He’s really a good guy. And he’s so young!”

Miliband returned the praise, telling Vogue: “She’s delightful to deal with one on one. She’s someone who laughs and can tease, and she’s got perspective as well.”

The emails released on Monday were the latest monthly instalment of messages that Clinton has turned over to the US state department from her private server.

Her use of a personal email account while in office has prompted a congressional investigation and led to her agreeing to make public around half the emails to and from her personal account, hdr22@clintonemail.com.