Anyone who has been to the British Library will have seen Bill Woodrow's sculpture, Sitting on History (1995) – a gargantuan bronze book, ball and chain – or in Trafalgar Square, his curiously similar bronze tree and book that crowned the Fourth Plinth in 2000. Public art is not normally renowned for its subtlety, since questions of accessibility, weather-resistance and pigeons tend to override more aesthetic concerns. And while such commissions are respectable milestones in an artist's career, the downside is often that their sense of social responsibility can start to dominate, and their work becomes correspondingly banal. 

The Royal Academy's survey of Woodrow's work from the late 1970s to his recent pieces provides a comprehensive illustration of such a shift, in an exhibition that chronicles his impressive early works followed by a gradual loss of edge and energy. While Woodrow first worked in "raw" materials (cut steel, fabric, concrete and plaster), found objects and appliances, his shift to bronze in the 1990s marks the peak of his artistic career. His recent works are sadly lacking in substance, mired in simplistic environmental commentary and blunt symbolism. 

Nevertheless, the exhibition forms a coherent narrative of Woodrow's development, and the first three rooms provide fascinating viewing. In the late 1970s, Woodrow seems a man obsessed with the natural world – and with sticks, in particular. The humble staff is the subject of Floating Stick (1972), a rather mesmerising video in which a large stick inexplicably floats about a country scene, evocative of the dowsing rod, or the old trick of dangling a carrot, fisherman-like, ahead of your donkey to keep him moving.

Strongest, however, is the work from Woodrow's late-1970s and 1980s "Breakdown" and "Cut-out" series. Household appliances such as radios or vacuum cleaners are broken apart, their constituent parts laid out in meticulous arrangements from tiny pins to plastic casing (specially reconstructed for this exhibition). Woodrow also fossilised telephones and carpet cleaners under thick layers of plaster, styled to look like rock, as if these everyday objects were strange artefacts, discovered centuries later. The Long Aspirator (1979), in which a vacuum tube is laid out horizontally and covered in rock-plaster, playfully metamorphoses this domestic object into a shape that suggests a boa constrictor.

Woodrow's work with filing cabinets, television sets and washing machines are proof of his incredible skill with airplane shears. His intricate cuts have pulled a bicycle frame out of the casing of a spin dryer (Spin Dryer with Bicycle Frame Including Handlebars, 1981) – and the fact that he shows you exactly how it's done, so that you can trace back the entire frame to one continuous cut in its "host" object, makes it all the more impressive.

In these works, Woodrow's sense of humour, skill and transformative power is in full force. There is grit in his use of industrial materials and destroyed consumer goods, and there is tantalising mystery in narrative pieces such as Red Monkey (1985): just what is going on with this sinister monkey, dropping bowling balls and a handgun off his perch on a filing cabinet? It's a shame, then, that in the next room, Woodrow's late 1980s and 1990s work leaves behind this sense of youthful edginess, and matures into his slick bronzes.

Sculpting in bronze was, apparently, considered a radical break from Woodrow's contemporaries, who saw this medium as too laden with tradition. But despite sticking his fingers up at the establishment in the ironic sculpture of a war veteran, For Queen and Country (1989), Woodrow's 1990s pieces tend more towards the conventional. They are as shiny and colourful as Venetian glass, and somehow too contrived. Though leaving behind the stick-fetish of his early years, Woodrow returns to organic forms in this period, and has by this point developed a serious obsession with bees and beekeeping. Beekeeper and Four Hives (1997) shows a fragile wood-puppet beekeeper, proceeding precariously towards his hives along a beam: but there are too many fussy extensions protruding from the piece's central pillar, giving it a weathervane-like appearance. 

The final room showcases Woodrow's sculptures and paintings from the last decade, which engage with such vast themes as the fall of mankind and the impact of oil dependence on the natural world, and on the native populations of the far north. I doubt anyone will miss the belaboured point of his Black and White series (2012) depicting Inuit figures atop shiny black oil spills; or the smug cleverness of Eye Two Eye (2012) in which a pair of binoculars is transformed into a pair of ancient fertility figurines, linked by a conspicuous snake. Sticks also make a nostalgic reappearance – this time gilded in gold leaf – but otherwise, this late body of work left me rather cold. 

The exhibition is certainly worth a visit, however, for a retrospective on the earlier work of an important British sculptor – just don't breeze through the first two rooms. The Royal Academy certainly didn't save the best for last. 

Bill Woodrow RA, at Royal Academy of ArtsKate Mason's review of Bill Woodrow RA at the Royal Academy of Arts, London.3