When Blossoms spoke to the Guardian in 2016, they revealed that their wildest fantasy would be to have a set of road signs in their home town, reading: “Welcome to Stockport: home of Blossoms.” Just two years later, the signs are in place, courtesy of the council. The band’s name is also emblazoned on the back of struggling Stockport County FC’s Edgeley Park stadium and in front of the vintage Wurlitzer organ in this beautiful art deco cinema.

In between, there have been two top five albums (including a No 1 with their eponymous debut) and gigs at Wembley Stadium with the Stone Roses, which would have been the stuff of dreams when they were rehearsing in a scaffolding yard and making videos for £60.

Along the way, they have transformed from a vaguely psychedelic indie guitar band with bowl cuts into a full-on, shiny, keyboard-dominated pop thing. Where their guitar-based music once had echoes of Pink Floyd, their luxuriant synth-pop now shares DNA with the likes of A-ha, the Human League and Abba. Named after a nearby pub, Blossoms may look like regular northern lads, albeit with hippy hair, but their sound owes much to the kind of keyboard-heavy 80s pop bands with daft names who would gaze moodily into the middle distance under elaborate New Romantic coiffures.

Wistfully euphoric opener There’s a Reason Why (I Never Returned Your Calls) and the beautifully lovelorn How Long Will This Last? relocate New Order’s old G-spot on the cusp of agony and ecstasy and set the scene for a steady procession of singable, summery synth-pop.

This two-night homecoming – which kicks off a tour to promote the new album Cool Like You, which charted at No 4 – inevitably, feels like a celebration. Blossoms come on to Frankie Vaughan’s song Stockport, and when vocalist Tom Ogden says, “Good evening, Stockport, we are Blossoms from Stockport”, you fear for the building, although he doesn’t overplay the local heroes card.

Apart from shouting “Have we got a rowdy balcony?” (which quakes in approval), they mostly just get on and play the songs – 18 of them, with 10 from the new album. On record, Myles Kellock’s fairground keyboards are ramped up for the radio, so it’s nice to hear subtleties such as Charlie Salt’s Chic basslines.

Doorsier old songs such as Blow or Cut Me and I’ll Bleed could be a different band, but demonstrate that even when Blossoms were dressing like the Rutles, they had the devotion to verse, chorus and middle eight that is the hallmark of a singles group. Strip away the electronics and I Just Imagined You could be the 1960s Hollies. The deluxe version of Cool Like You does unplug the synth – for lovely acoustic, campfire versions of the songs that are closer to Fleet Foxes than Duran Duran. When Ogden dons an acoustic guitar for a solo spot here, his own Love Talk more than holds its own in a singalong covers medley that hurtles from Baby Bird’s You’re Gorgeous to George Michael’s Last Christmas. The synths are plugged back in and Charlemagne’s big, bouncy riff – the blueprint for Blossoms 2.0 – completes the celebrations in a town that is audibly delighted to have something to sing about.

• At O2 Academy, Leeds, tonight. Box office: 0844-477 2000. Then touring.