Three cheers for excellent ordinary architecture. Five of the six buildings shortlisted for British architecture's annual Oscar, the 2015 Riba Stirling Prize, haven't got a trace of designer bling about them. There is a faint odour of political correctness about the selected projects, but the key thing is that most of them serve ordinary people, and ordinary daily life.

Britain's best buildings in 2015 are Burntwood School in Wandsworth, designed by Allford Hall Monaghan Morris; the Peabody affordable housing block at Darbishire Place in east London, by Niall McLaughlin; the Maggie's cancer care centre in Lanarkshire, by Reiach and Hall; the NEO Bankside luxury apartments in Southwark, Rogers Stirk Harbour; the library and teaching building at the University of Greenwich, by Heneghan Peng; and the Whitworth Art Gallery in Manchester, by MUMA.

The Royal Institute of British Architects' judges have obviously taken the greatest care to tick a wide range of democratic boxes, and its president, Stephen Hodder, says: "The shortlisted projects are each surprising new additions to urban locations – hemmed into a hospital car park, in-filling an east London square, completing a school campus. But their stand-out common quality is their exceptionally executed crafted detail."

Only one project on the shortlist, NEO Bankside, had a big price tag, £140m. The rest were low-cost, or very low-cost, buildings. The message sent by this shortlist is a good one: that there is no reason why ordinary building types can't be well designed and well built.

Riba Stirling Prize 2015 shortlist Show all 6 1 /6 Riba Stirling Prize 2015 shortlist Riba Stirling Prize 2015 shortlist Burntwood School, Wandsworth, London This project, by AHMM, was discussed at some length by the jury for the Architects Journal’s Best Building in 2015. It didn’t win, but there was no doubting the architectural ambition of the scheme. Tim Soar/PA Riba Stirling Prize 2015 shortlist Whitworth Gallery, Manchester The MUMA practice opened a new central axis through the original Victorian building and added an L-shaped glass box to the side of the building facing Whitworth Park. Brilliant! But then they put brick “stitches” along one flank, signifying the city’s historic cotton industry. They don’t. They just look silly. And there are polished steel columns in the glass-sided restaurant, to reflect the trees in the park. Equally silly. Alan Williams/PA Riba Stirling Prize 2015 shortlist Library and teaching building, University of Greenwich The Irish practice Heneghan Peng gave this building a skilfully modulated form and facades, decreasing its sense of mass, and fitting it into its urban context. Wierdly, if you shrink a segment of it, it recalls the St Andrews housing by the Scots, Sutherland Hussey. Hufton + Crow/PA Riba Stirling Prize 2015 shortlist Maggie’s cancer care centre, Lanarkshire Reiach and Hall’s design takes the form of a building and courtyard. There is absolutely nothing look-at-me about it. What it does convey is a place of retreat and calm order. No, Maggie’s centre has quite equalled the brilliantly “domestic” one designed by Rogers Stirk and Harbour at Charing Cross Hospital. Nevertheless, the Lanarkshire building is very much in that homely mode. David Grandorage/PA Riba Stirling Prize 2015 shortlist NEO Bankside, Southwark, London Or is it NEO Blingside? The apartments cost between £1.5m and £4.5m. The Meccano-like buildings have the brio of Rogers Stirk Harbour’s trademark steroidally expressed, brightly coloured structure and exoskeleton. The materials, finishes and details are superb. But if the judges were being picky, they might recall that the ‘Architects’ Journal’ criticised the fact that some of the exposed structural bracing was just for show. Edmund Sumner/PA Riba Stirling Prize 2015 shortlist Peabody affordable housing, Darbishire Place, London Most people would find Niall McLaughlin’s design unremarkable. Bricks, simple balconies, a regular architectural rhythm, nothing much to catch the eye – all very self-effacing. But compared to the premium-value apartment blocks mushrooming across London this is virtuous ordinary architecture for those who earn something like the London pre-tax average of £34,000. Nick Kane

That kind of architectural quality is often mistakenly associated with so-called "landmark" or "iconic" buildings. Most of them are luridly banal architectural tumours implanted in the fabrics of our towns and cities to create commercial or cultural hot spots to keep most of us in shopping and entertainment modes – rather than fretting about, say, the possible need to live in one of the 4 by 5 metre micro-housing units coming on to the market in London, where housing classed as affordable can cost as much as 80 percent of the open market value.

The Stirling Prize shortlist may not be controversial, but several architectural practices will certainly feel that they have missed out because the list is so dutiful. If the shortlist had been aimed at highly refined architecture, the WWF headquarters in Woking, designed by Hopkins Architects, would have been selected. So might Duggan Morris's small, rivetingly angular school swimming pool building in Beaconsfield.

And if there was ever an example of being almost too good in a specific field, it's Haworth Tompkins, whose improvements to the National Theatre are exemplary. Alas, they won the Stirling Prize last year with their superb Everyman Theatre in Liverpool. They're obviously not allowed to get anywhere near the chocolates two years in a row.

Among the education projects that might have made the cut in other years are Feilden Clegg Bradley's Students Union at Manchester Metropolitan University, and John McAslan + Partners' typically taught engineering building at Lancaster University. Among the housing projects, Sutherland Hussey's West Burn Lane scheme in St Andrews is exceptional skilled in the way it inveigles modern architectural form into a conservation area in a famously conservative town.

And if there's a practice that has every right to feel hard done by, it's Lifschutz Davidson Sandilands, whose two London buildings on the Stirling longlist – the transformed Foyles book store, and the remodelled Bonhams auction house – are outstanding in their architectural clarity, internal atmospheres, and finessed details.

And so, who will win the Stirling Prize on October 15? The bookies favour the Maggie's Centre. But it's a tough call. If the judges max out on political correctness, it could be the Peabody Housing, or the University of Greenwich Library. If they veer towards something a shade more cultural, Manchester's Whitworth Gallery could triumph, despite having a couple of distinctly peculiar architectural features.

Whitworth Gallery, Manchester

The MUMA practice added an L-shaped glass box to the building (PA) The MUMA practice opened a new central axis through the original Victorian building and added an L-shaped glass box to the side of the building facing Whitworth Park. Brilliant! But then they put brick "stitches" along one flank, signifying the city's historic cotton industry. They don't. They just look silly. And there are polished steel columns in the glass-sided restaurant, to reflect the trees in the park. Equally silly.

Peabody affordable housing, Darbishire Place, London

Peabody affordable housing is virtuous ordinary architecture for those who earn something like the London pre-tax average of £34,000 (PA) Most people would find Niall McLaughlin's design unremarkable. Bricks, simple balconies, a regular architectural rhythm, nothing much to catch the eye – all very self-effacing. But compared to the premium-value apartment blocks mushrooming across London this is virtuous ordinary architecture for those who earn something like the London pre-tax average of £34,000.

NEO Bankside, Southwark

NEO Bankside has the brio of Rogers Stirk Harbour's trademark steroidally expressed, brightly coloured structure and exoskeleton (PA) Or is it NEO Blingside? The apartments cost between £1.5m and £4.5m. The Meccano-like buildings have the brio of Rogers Stirk Harbour's trademark steroidally expressed, brightly coloured structure and exoskeleton. The materials, finishes and details are superb. But if the judges were being picky, they might recall that the 'Architects' Journal' criticised the fact that some of the exposed structural bracing was just for show.

Library and teaching building, University of Greenwich

The University of Greenwich's library features skilfully modulated form and facades (PA) The Irish practice Heneghan Peng gave this building a skilfully modulated form and facades, decreasing its sense of mass, and fitting it into its urban context. Wierdly, if you shrink a segment of it, it recalls the St Andrews housing by the Scots, Sutherland Hussey.

Maggie's cancer care centre, Lanarkshire

Reiach and Hall’s design conveys a place of retreat and calm order (PA) Reiach and Hall's design takes the form of a building and courtyard. There is absolutely nothing look-at-me about it. What it does convey is a place of retreat and calm order. No, Maggie's centre has quite equalled the brilliantly "domestic" one designed by Rogers Stirk and Harbour at Charing Cross Hospital. Nevertheless, the Lanarkshire building is very much in that homely mode.

Burntwood School, Wandsworth, London (pictured top)

This project, by AHMM, was discussed at some length by the jury for the Architects Journal's Best Building in 2015. It didn't win, but there was no doubting the architectural ambition of the scheme.