A mesmerising wooden mosque in Cambridge will go head to head with a Cornish footbridge and a cluster of black boatsheds in the Lake District, in this year’s battle for the UK’s best new building. Joining them in the race for the 2021 Riba Stirling prize are a new student centre for Kingston University, a key worker housing development in Cambridge, and a controversial stone apartment block in London which was almost demolished by the local council.

The mosque is the list’s photogenic stunner, and the most likely to snatch the gong. Designed by Marks Barfield, architects of the London Eye ferris wheel, it applies hi-tech rigour to the creation of a beguiling glade of worship. A grid of tall tree-like columns branch outwards, weaving into a filigree structural canopy that undulates above the prayer hall, echoing the form of gothic stone vaults, and filtering daylight from circular openings above. Featuring Cambridge Gault clay brickwork, patterned with decorative Arabic Kufic inscriptions, and ablution facilities worthy of a luxury spa, the GBP23m building is a compelling fusion of local and Islamic traditions, creating a powerful prototype for what a modern British mosque might be.

An equally startling reinvention of a familiar type comes in the form of the Tintagel Castle footbridge. Spanning a dramatic gulch that separates the Cornish mainland from the site of Arthurian legend, the gossamer bridge shimmers like a dewy spider’s web spun across the ravine. The GBP5m structure looks impossibly slender, tapering to nothing at the centre, where the two cantilevered halves meet with a narrow gap. Designed by Belgian bridge specialists Ney & Partners, with William Matthews (who led the design of the Shard skyscraper for Renzo Piano), it has an unusually handcrafted, tactile quality for a piece of infrastructure. The handrails are made of raw oak, while the deck is surfaced with local slate tiles, packed together on their edges without mortar, giving the pleasing sense of walking across a box of After Eight mints, above the crashing waves.

A similar mix of raw and refined is found at the Windermere Jetty Museum in the Lake District. Designed by Carmody Groarke as a demure cluster of black metal sheds, the GBP20m complex is a refreshing departure from the national park’s usual insistence on drystone walls and slate roofs. Taking inspiration from boathouses and nearby agricultural barns, the sheds’ black-oxidised copper walls glimmer with a faint verdigris patina, while chunks have been carved out of their sides, leaving rooftops floating with surreally deep overhangs. Lined with warm Douglas fir timber, echoing the sleek pleasure boats on display, the buildings are carefully composed to frame views of the lake, allowing water to lap inside the building at some points – bringing with it curious swans and otters.

The lengths to which universities are now going to attract applicants in an increasingly competitive market is evident in Kingston’s GBP50m Town House, a palatial new student centre in London. Designed by Irish Pritzker Prize winners Grafton, the building combines a library and dance studios into a dynamic, multi-storey cathedral of collisions and connections. Quiet study areas enjoy vertiginous views into the central performance space, while a broad staircase meanders through the building, leading to a rooftop cafe with panoramic vistas across to Hampton Court Palace and the Thames. A series of connected balconies cascade around the concrete-framed facade, adding to the sense of the building as an open “learning landscape”, designed to encourage chance encounters with fellow students – which sounds like a welcome prospect after months of online learning.

After a bold council housing scheme in Norwich won the last prize in 2019, this year sees a rather dull Cambridge University-funded housing project grace the shortlist. Part of the new Eddington suburb, the key worker flats by Stanton Williams are inspired by the form of the city’s hallowed college courts. The buff brick blocks form a series of loose, interconnected courtyards, tied together with richly varied landscaping designed by J&L Gibbons, which helps to soften the stark architecture.

It is well made, with neat bike sheds and innovative underground bin storage, but there is something stultifying about the overall effect. It is a relentlessly beige, lifeless place – perhaps in thrall to the legacy of Accordia, the 2008 Stirling prize-winning housing development on the other side of town, which has loomed large over much housing of the last decade. One of Peter Barber’s quirky social housing projects would have made a more interesting inclusion on the shortlist (his projects have been confined to the separate Neave Brown award for housing instead, where they comprise two of the four contenders).

Finally, to spice things up, comes a wildly original building that Islington council did its best to have bulldozed. From a distance, 15 Clerkenwell Close looks like something Fred Flintstone might have erected after glimpsing the work of Mies van der Rohe. Its facade is a square grid of columns and beams, but the pieces are monolithic chunks of limestone, prised fresh from the quarry, their faces variously sawn smooth, cleaved or drilled, still showing their masons’ marks. These days stone is mostly reduced to a thin decorative cladding, but here it is doing the job of holding the building up – which, says its architect and developer Amin Taha, is cheaper, faster and embodies far less CO2 than an equivalent structure in steel or concrete.

It is a wonderfully poetic sight, a modern ruin with creepers now winding their way up the rugged stone frame. A fallen column, with a half-finished ionic capital carved into its rough face, leans by the entrance, the spiral carving echoing the form of an ammonite protruding from a slab above – an allusion, like the bronze scallop shells that decorate the gates, to a nunnery that once stood nearby. From the glass-box meeting room resting on an I-beam above Taha’s basement office, to the intricate folding, sliding cabinetry of the apartments above, to a clever glass-topped lift shaft that does away with the need for bulky mechanical ventilation, an obsessive level of thought has gone into every detail.

None of this was enough for the council, which declared the GBP5m building to be “rough, ugly and detrimental to the conservation area,” and served a demolition notice, claiming it was in breach of its planning permission. After lengthy legal wrangling (which delayed its Stirling shortlisting since 2018), a planning inspector found in favour of Taha.

It would be sweet revenge for this neo-neolithic masterpiece to win the prize, and its level of craft and innovation is certainly worthy. But, for all its merits, it is hard to see the judges opting for a bespoke private fantasy of eight luxury flats over a project that makes a wider public contribution. My money is on the mosque, a modest thing from the outside, which contains one of the most entrancing interior spaces built this century, a King’s College Chapel ceiling for our new timber age.