By Gergely Szakacs and Fedja Grulovic

BUDAPEST, June 27 (Reuters) - More than 10,000 Hungarians on Saturday joined Budapest's first annual Pride march since right-wing ‌leader Viktor Orban's election defeat in April, braving record heat in ‌the city to walk with huge rainbow and European Union flags.

Last year's march, which Orban tried to ​ban as part of his wider policies targeting LGBTQ+ rights, turned into a mass anti-government demonstration that attracted tens of thousands of people.

This year, after Orban's defeat to Peter Magyar's centre-right Tisza party, the ban was lifted and the march cleared ‌to go ahead.

Fanni Fajth, an ⁠18-year-old student, said the mood was much more optimistic after the political change in the country, and due to hopes for ⁠new rights related to adoption, and marriage in the future.

"Everyone is just so much more uplifted," she said.

"I think it would be wonderful if we just had equal ​rights ​finally after all these years."

Orban, who cast ​himself as a defender of what ‌he called Christian values from Western liberalism, passed laws ending the change of gender in personal documents, halting adoption by same-sex couples and banning materials in schools seen as promoting homosexuality or gender transition.

"The biggest change is actually the change in politics in the country," said Mate Tarnai, a 51-year-old chemist. "We feel more ‌freedom personally as well, and also the atmosphere ​in the country is much more relaxed ​than last year."

Tarnai also said he ​hoped for equal rights from Magyar's government.

Magyar, a conservative, has ‌asked for patience when asked by ​Hungarian media about changing ​legislation that curtailed the rights of the LGBT community.

Boglarka Boruzs, 23, an interpreter and translator, said for her the biggest change from Orban's rule ​was that LGBTQ+ people could ‌feel safer and more accepted in everyday life, and politicians held ​the power to "make society understand that it's okay to be gay."

(Reporting ​by Gergely Szakacs; Editing by Alexandra Hudson)