The Budapest Festival Orchestra never stops proving what a great ensemble it is. In last night’s concert, the third Prom of its weekend residency, the miraculous ways in which the absurd humour of Ligeti, the deep soulfulness of Bartók and the implacable genius of Beethoven were brought to the surface were not just joyful and completely fulfilling, but also unfailingly drew in the attention of the whole audience in a completely full Royal Albert Hall.

It would be worth travelling a long way to hear the Budapest Festival Orchestra giving such a lithe, athletic performance under its founder and Music Director Iván Fischer of Glina’s Ruslan and Lyudmila Overture. That was the Radio 3 and Proms Audience Choice from 19 overtures and preludes whittled down to three. What happened next, despite some equally lustrous playing, didn’t always work so well.

“Very traditional, but fun,” ran the verdict of one fellow-traveller as we waited for a bus outside the Royal Albert Hall on Saturday night. No one can gainsay the infectious fun that the Budapest Festival Orchestra bring to every gig. For all its musical accomplishment, Iván Fischer’s all-singing (yes, they did) if not quite all-dancing (yet) outfit never forget that they belong to a, rather elevated, branch of show business.

“There will be more incense,” promised Glyndebourne Music Director Robin Ticciati of the company’s annual visit to the Proms. He was talking to my Opera Zoom class between the final rehearsal and first performance of Poulenc’s great masterpiece about the martyrdom of Carmelite nuns during the French revolution, as directed by Barrie Kosky with unsparing horror and humanity. And now here was the operatic company of the year taking its final bow after a sellout run in Sussex.

Programming works from the same decade – in this case the 1940s – can reveal fascinating contrasts: what an impressive gulf, for instance, between two masterpieces by Hindemith and Strauss in this first half, and what sensitivity to very different styles from the NYOGB under Carlos Miguel Prieto. Be careful what you choose as the big symphony, though. I’d always had my doubts about Copland’s Third, and though it couldn’t have been more compellingly lit and shaped, it paled by comparison.

One of the undoubted highlights of Prom 14 was unprogrammed – following his commanding performance of Beethoven’s third piano concerto, Jan Lisiecki returned to the stage to give an encore of Chopin’s Nocturne in E Flat, Opus 9 No 2.

This Prom by the BBC Philharmonic was billed as a celebration of the 50^th anniversary of the Royal Northern College of Music, in distant Manchester.

Pekka Kuusisto, making his Proms debut as conductor in the first half of this concert, and then as violinist/conductor/ringmaster/energiser in the second, brought lightness, playfulness, and a Finnish sense for the absurd to the Albert Hall. He is an absolutely live-wire performer and has a hugely charismatic musical presence. He radiates joy in his craft and also unfailingly communicates his appreciation for those around him.

Even before the Just Stop Oil protesters hit the stage after the interval, this was destined to be one of the most politically charged Proms the Royal Albert Hall has witnessed for a while. The rousing cheer that greeted the BBC Singers was hopefully all the beleaguered BBC bosses needed to realise – after the ill-advised attempt to abolish them in March – what a key part of our music culture they remain today.

Flying manes and flashing eyes are part of the inspirational package. We may laugh at some of these dramatic images, but it's usually a sign of the conductor's commitment to his or her orchestra and audience. There's no doubt that the Royal Albert Hall from July to September is a place where magic can happen, even if it's as unpredictable as the acoustics of the capricious venue itself.