Richmond Theatre, The Green TW9

The classical lady with the wardrobe malfunction on the front of Frank Matcham's theatre is Euterpe, 'Giver of Delight', the muse either of music or lyric poetry depending on your preferred myth. She carries an aulos or double flute, the instrument she invented (or not, again depending on your source).
The figure was modelled by John Broad and supplied by Doulton in Lambeth, who supplied another copy for Matcham's Hackney Empire.
Broad modelled Euterpe again for the Apollo pub in Tottenham Court Road, the statue ending up in St George's Gardens.
The rest of the terracotta work on the facade was supplied by the Hathern Station Brick and Terra Cotta Company, including this mischievously satirical face.

Terrace Gardens, Richmond SW13

Terrace Gardens contain two distinguished works of art. At the bottom of the hill close to the river stands a statue of Old Father Thames, a 1775 copy in Coade stone of an original by John Bacon the Elder. The god reclines on a block of stone, a floral wreath on his head, pouring the river waters out of a jar. It is a fairly standard classical production of the sort Bacon excelled in - there are other copies at Ham House and Somerset House.
At the top of the hill is a pond that used to surround a cast iron fountain that was taken away for salvage in WW2 (although rumours persist that, being difficult to recycle, it was in fact dumped in the river). To fill the space, in 1952 the sculptor Allan Howes presented the borough with a statue of Aphrodite that had been exhibited at the Royal Academy. Although Howes lived in Hammersmith, his wife was born in Richmond.
The Goddess of Love, uncompromisingly nude, sits on the head of a dolphin carrying a conch. Her robustly-proportioned body is built up of simple, almost geometrical shapes.
This being the 1950s, it caused a storm.The Richmond and Twickenham Times ran no fewer than 84 letters describing her as an insult to the female form and calling for schoolchildren to be banned from looking at her. One letter sneeringly described her as 'Bulbous Betty', a nickname that, of course, stuck.
Another correspondent wrote: "The sculpture is as disturbing to gentlemen as Father Thames is to maidens," though what evidence he had for that assertion is unknown.
The council voted for her removal, but eventually the will of the tolerant but non-local-paper-letter-writing majority prevailed and she remains to delight us still.
But even the official plaque in front of her describes her as Bulbous Betty, poor girl.

Former Cooperative Store, 161 Bow Road E3

The skep, a beehive made of straw, was a powerful symbol of harmony in the workplace for early utopians such as Robert Owen and the founders of the Co-operative movement.
Technically, the design was already obsolete in 1919 when this shop was built by the surveyor to the Stratford Co-operative Society, HE Tufton. Its lack of an internal structure for the honeycomb made it difficult to extract the honey, and the process often killed all the bees. But it looks pretty. The fence behind and the flowers growing up beneath add a rustic touch.

Idea Store, Gladstone Place E3

The trendily-branded Idea Store was built as the Passmore Edwards Public Library in 1901, to a charming Queen Anne style design of Samuel Russell.

When the library was done over in 2007, the original front door was replaced by a new one further along leaving it looking somewhat redundant, but it is worth seeking out because it is surmounted by a flamboyant carving of a man and a woman in fanciful old-timey costumes holding up a shield with the Passmore Edwards name. 

The work is attributed to Henry Fehr, and indeed the flowing lines and almost Art Nouveau look are characteristic of him. As he was also Russell's favourite artist, the attribution seems pretty secure.

Whitechapel Art Gallery, Whitechapel High Street E1

The front of the Whitechapel Art Gallery was a flat, unadorned wall for more than a century after it was completed in 1901.

As designed by Charles Harrison Townsend, it was going to frame an allegorical mosaic by Walter Crane but the philanthropists backing the project fell out and it was never executed. The only decoration was the interlocking foliage by Walter Aumonier.
In 2012, a new artwork called Tree of Life was commissioned from Rachel Whiteread as part of the Cultural Olympiad. She covered it with gold leaves, four central blocks providing a pivot for the design.
In 2007 the gallery expanded into the former Passmore Edwards Library (1892) next door, having reconstructed it internally and restored the facade, including the rather charming terracotta work includind a putto over the main window and friezes with cherubs, by E. Caldwell Spruce of Burmantofts Art Pottery in Leeds.
As a final touch, a weathervane by the Canadian artist Rodney Graham was popped on the tower. . Called Allegory of Folly, it depicts Erasmus reading his master work, In Praise of Folly, while riding backwards on a horse. There is a story that the great humanist wrote his famous attack on superstition while riding from Italy to London, but there is an alternative account that says he wrote it in a week at Sir Thomas More's house.
The figure is in fact Graham himself, dressed in Renaissance schmutter and clutching the Vancouver telephone directory. It is an idea he has played with before, in a windvane of himself riding a bicycle backwards.

Trinity Hospital, Mile End Road E1

The lovely Trinity Hospital was built by the lights-and-buoys authority Trinity House in 1695, not for medical purposes but as almshouses for '28 decayed Masters and Commanders of Ships, or ye widows of such.'

The street facades are ornamented with highly detailed models of 42-gun warships of the 4th Rate. The ones you see today are fibreglass copies made when the almshouses were restored by the Greater London Council in the 1950s - the originals are now in the London Museum.

Carved in marble by Robert Jones, the ships are typical of the Stuart period with flamboyant decoration and big windows in the captain's cabin. The museum says: "The models are thought to be unique and of particular historical interest because they portray English warships of the late 17th century with great accuracy. Microscopic examination has shown that the ships have been painted black twice in the past (on one occasion to mark the death of Lord Nelson)."
Ships of the 4th Rate were not inferior in some way - the great Samuel Pepys as Secretary of the Navy had introduced the classification system both to determine if a ship was powerful enough to take part in pitched battles and also to determine the rate of pay of the crew. A ship of the 4th rate was, in Pepys's system, a ship-of-the-line mounting between 38 and 62 guns.

The models are larger than they look from the ground - more than 1.1m high and 1.2m long.

(Thanks to Hazel Forsyth at the London Museum)