Brian Eno likes the Leisure Society. So does Ray Davies. These facts alone are reason enough to persuade anybody to go and see a band. A listen to the Leisure Society on Spotify ought to dispel any lingering hesitation. Their music is compulsively listenable, easy on the ear, musically clever without being pretentious, lyrically versatile and emotionally complex. If you’re not persuaded, then here’s another fact: their members include a flautist and a violinist as well as the usual suspects.

The band were performing at the Bullingdon as part of a tour to promote their latest album, Arrivals and Departures. It’s their fifth album, in the works for four or five years, and it tracks the break-up of the relationship between the band’s lead singer (Nick) and flautist (Helen). It charts every stage of the process, from anger to confusion and on into resignation and separation; Nick wrote most of the songs while living out of his suitcase. Both Nick and Helen are still members of the band, but Helen wasn’t part of the touring group. Nor were any of the band’s ad-hoc members. They were reduced to the essentials: bass, synth, drums, electric guitar and violin. The result was a cleaner, leaner and more powerful sound than you’ll hear on their recordings.

The band had just arrived from Dublin and were, said Nick, ‘a little delirious’. I was also a little bit delirious as I had forgotten to eat anything. An unfortunate side effect was that I found myself continually reaching for food similes. My conclusion? The Leisure Society are the musical equivalent of a really satisfying cheesecake. They’re built on a solid, gingernutty base of guitar and drums; Nick’s voice is thickly layered on top like ricotta mixed with cream; Mike’s violin, with its plucked notes and flights of vibrato, is like lemon zest grated over the top. It adds colour and a certain twanginess when played pizzicato.

You know what you’re going to get from a cheesecake. It will probably taste of cream, cheese and biscuit. Similarly, you know roughly what to expect from a song by the Leisure Society. They are purveyors of happy mellifluous melancholy, of songs with sumptuous melodies, a strong rhythm, longing lyrics, and the hum of a violin. They have, in other words, a trademark sound. You can’t fail to recognize them once you’ve heard a couple of their songs.

A classic example is ‘The Last of the Melting Snow’, the first song from their first album, which is as gentle and melancholic as can be. ‘Save it for Someone Who Cares’, also from their first album, is an alternative archetype. It begins with some fluttering from the flute before the beat breaks in (dum-da-dum, dum-da-dum). Then the words come. At the end of the song, the band launch into a series of up-down, country-sounding scales accompanied by rhythmic clapping and some long trills on the violin. Another song in a similar but different style is ‘Fight for Everyone’ which, with a few lyrical adjustments, could serve as a Corbynite anthem. It’s gloriously upbeat and infectiously optimistic, opening with a simple trumpet melody and building into an expansive tune based on a series of overlapping keyboard riffs and a meandering synth. It’s almost too easy on the ear, too musically unadventurous. Still, it’s fun. I can guarantee that everybody in the crowd enjoyed it when it was played, myself included

Many of the songs on Arrivals and Departureshark back to these models, but others spring surprises. In the middle of one song, Mike flipped his violin over and started strumming it as though he’d mistaken it for a guitar. He did, in fact, switch to electric guitar for a couple of songs. ‘Mistakes on the Field’ begins slowly with variations on an arpeggio; then in come the guitars and trumpets; then the synth starts again with its six note, up-down arpeggio. Eventually we get some simple lyrics. In the last minute, the guitars are set loose. There’s a gap – people clap, they think it’s all over – and then the band play a two-minute instrumental. The sound here is denser and less pastoral.

I found myself paying particular attention to the lyrics, which are are quick-witted and occasionally approach the almost-poetic. ‘ ‘Leave me to Sleep’ even finishes with a snatch of poetry from Liz Berry, a Black Country poet perhaps best known for ‘The Republic of Motherhood’. The combination works perfectly: the notes end and the words continue, a resonant echo of what came before. Of course, not all of the songs are particularly elevated. ‘We were Wasted’ was directly inspired by a particularly memorable night out in Burton-on-Trent, the band’s hometown.

The Leisure Society are the sort of band who always get four-star reviews. Disliking them is virtually impossible. I’ve tried to induce it under laboratory conditions, with little success. Nonetheless, reviewers usually have reservations. Aren’t they a bit too safe, too same-ish, too sweet, like Marmalade made without Seville oranges? These are valid complaints, but I have no qualms in awarding the Leisure Society five stars. I could say something like ‘their most recent songs add musical texture and emotional seriousness, improving…’ But the real reason is this: They made me deliriously happy for an entire sixty minutes. What else can I say, except listen to this?