Ten years ago, no one hung around in Trafalgar Square for long unless they had a high tolerance of pigeons.

What the Square offered was Nelson’s Column, four metal lions, a set of two fountains and a flock of birds so dense and fat on grain that a child could get lost in a flapping, cooing cloud of semi-domesticated feathered vermin.

A child can get lost in Trafalgar Square again this week. In fact, they are meant to, because on a part of the square which would once have been thick with pigeon droppings there is a maze.

As a maze, it hardly competes with the one in Longleat in Wiltshire, which has nearly two miles of paths between rows made of 16,000 yews. Trafalgar Square’s temporary maze covers an area of about 450 square metres, and though the notice at the entrance invites you to “get lost in the West End”, it takes only a couple of minutes to find your way past the three or four dead ends.

That has not stopped the visitors pouring in. The maze opened yesterday, and in little more than two hours, 2000 visitors had passed through.

Its special feature is that each section has a street sign bearing the name of a famous street in the West End, and a blue plaque outlining the history of the street. For the most part, “history” means cultural events that have taken place within the lifetime of the average grandparent. You can find out, for instance, where and why Maurice Micklewhite changed his name to Michael Caine, or on which street The Beatles gave their last live performance – but there is also an occasional nugget from further back in time, such as the name of the first English trader to sell grapefruit.

The maze, which was created by the West End Partnership, an umbrella organisation that promotes theatreland and its assorted entertainments, is one sign of the way that Trafalgar Square is a very different public space from what it used to be when it was home to one of the largest and fattest concentrations of pigeons anywhere in the world.

The main amusements back then were feeding these indulged birds. There was a famous character named Bernie Rayner who ran a stall selling little packets of grain which tourists bought at an inflated price to feed the equally inflated pigeons. They fed so well that they bred several times a year. Repairing the damage to Nelson’s Column caused by pigeon droppings cost £140,000 ($304,000).

But when Ken Livingstone was elected as London’s first mayor, in 2000, he was prepared to invest £25 million in making the capital’s most famous square a more attractive place to congregate, with its north side closed to traffic and made into a pedestrian area, and with a cafe and new public toilets added. His plans included a declaration of war on the 4000 pigeons.

The Greater London Assembly passed a bylaw making it illegal to feed them and introduced hawks to frighten them away, and council staff made periodic raids with giant vacuum cleaners to hoover up any food from the square’s smart new paving stones.

The campaign provoked outrage from bird lovers, and from Bernie Rayner, who tried to obtain a High Court order to protect his business. A pressure group, Save the Trafalgar Square Pigeons, sprang up.

In the end the mayor got his way, and Trafalgar Square entered its post-pigeon era, where people could walk, sit, eat, and watch their children play without being dive-bombed.

What has probably attracted more interest than anything else is the celebrated fourth plinth. It was erected early in Queen Victoria’s reign to hold a statue of William IV, but – to London’s enduring good fortune – the funds for the statue were never raised, and the plinth stood empty for a century and a half.

In 1999 the Royal Society of Arts launched the Fourth Plinth Project, making it a setting for a sequence of contemporary works of art such as the striking Alison Lapper Pregnant, a statue of the artist born with no arms and shortened legs. For six months, the plinth housed a fibreglass statue of New Zealander Air Chief Marshal Sir Keith Park, a hero of the Battle of Britain. Currently, it holds an 11ft (3.3m) sculpture called Nelson’s Ship in a Bottle by the Anglo-Nigerian artist Yinka Shonibare.