The Queen will be familiar with Terminal 5 already. It will have been hard to ignore the arrival of Britain’s largest covered space, on its own the sixth-biggest airport in Europe, from Windsor Castle, six miles (10km) west. Up close, though, what will she find?

Something she is quite used to, but which to the average British traveller is a revelation: civility. Terminal 5 has no cattle-market queues, no ceilings so low that they scrape your skull, no lean-to sheds. Call this a British airport?

Inside all is serene, with atriums, terraced decks like a cruise liner and 558ft by 1,312ft (170m by 400m) of roof leaping overhead. Beneath your feet lies not that BAA standard-issue, stained carpet, but elegant tiles.

But Terminal 5 is more engineering than architecture. The longest British planning inquiry stymied original plans by the architects Rogers, Stirk, Harbour and Partners for a beautiful, spacious building like the one they built for Madrid airport which won them the Stirling Prize in 2006.

Given (relatively) little space, Terminal 5 went up, not out. This is the world’s first skyscraper airport, built on seven levels, each one double or triple height.

Compared with BAA’s other airports it is a palace. But what it lacks is the elegant originality of great airports – Eero Saarinen’s TWA terminal at JFK, Rogers’s own Madrid. Terminal 5 might have cost £4.3 billion, but there was no cash for refinement. Blame a convoluted planning system and the highest construction costs in the world.

Want to see how to really do it? At Norman Foster’s Beijing airport, which opened last month, China got the world’s largest building, handing 90 million passengers, for £1.6 billion, planned and built in four years. You can’t beat a one-party state, Ma’am.

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