Tour and taste at Denbies Wine Estate near Dorking, England's largest single-estate vineyard by its own account

Walk the Surrey Hills village of Shere, with its Tudor cottages and the Tillingbourne stream

Climb Box Hill, the National Trust chalk hill above the Mole

Denbies, on the chalk above Dorking, bills itself as England's largest single-estate vineyard, planted on the south-facing slopes of the North Downs. Box Hill rises across the Mole with its zigzag road and the view south from the top, and Shere, a few miles west along the Tillingbourne, has its Tudor cottages and the stream running through.

The Surrey Hills: Denbies, Box Hill and Shere

Walk Richmond Park, the 2,120 acres Charles I enclosed for hunting deer, and find the herds

Climb King Henry's Mound in the gardens of Pembroke Lodge for the protected view of St Paul's Cathedral

Walk the Isabella Plantation in Richmond Park when the azaleas bloom in spring

Walk Bushy Park's Chestnut Avenue, Wren's approach to Hampton Court, to the Diana Fountain

Charles I brought his court to Richmond in 1625 to escape the plague and turned the hill above the town into a park for hunting red and fallow deer. At 856 hectares — 2,120 acres — Richmond Park is the largest of London's Royal Parks, and a national nature reserve, a Site of Special Scientific Interest and a Special Area of Conservation. From King Henry's Mound in the gardens of Pembroke Lodge, which may be a Neolithic burial mound, there is a protected view of St Paul's Cathedral; the legend that Henry VIII stood on it has no evidence behind it. Next to Hampton Court, Bushy Park has Chestnut Avenue and the Arethusa 'Diana' Fountain, laid out by Christopher Wren as a grand approach to the palace, and from the mid-19th century until the Second World War Londoners came out for Chestnut Sunday to see the trees in flower — a custom revived in 1993.

Richmond and Bushy: London's Deer Parks

Walk the public footpaths through the rewilded scrub

Look for white storks on their nests in the oaks

Listen for nightingales in the thorn thickets in May

Look for purple emperors around the sallows in July

Charles Burrell took over 3,500 acres of heavy Sussex clay at Knepp in 1983, tried for seventeen years to make it pay, and from 2001 began letting it go: fences down, longhorn cattle, Tamworth pigs, ponies and deer left to shape the land. It is the first major lowland rewilding project in England, and it has become a nesting stronghold for nightingales, a breeding hotspot for purple emperor butterflies and the site of the first white stork chicks hatched in Britain for centuries.

Knepp: The First Big Lowland Rewilding in England

Find the Iguanodon with its thumb spike on its nose

Walk the whole island circuit and count the extinct animals

See the Megalosaurus and compare it with what we know now

Walk the terraces of the old Crystal Palace site above the lake

Benjamin Waterhouse Hawkins built these life-sized models for the Crystal Palace park under the direction of Richard Owen, the anatomist who coined the word Dinosauria, and they were unveiled in 1854 — the first dinosaur sculptures in the world. They are wrong in ways that are now famous: the Iguanodon stands on four legs with its thumb spike on its nose. That is the point of them.

The Crystal Palace Dinosaurs: The First Dinosaurs Ever Built

Walk the rim path round the Devil's Punch Bowl

Climb Gibbet Hill and find the Sailor's Stone

Walk the line of the old A3, now returned to heath

Listen for nightjars churring over the heath on a summer evening, May to August

The Devil's Punch Bowl is a great hollow of heath and woodland east of Hindhead, nearly 700 acres of it, cut by springs into the greensand. The A3 used to run round the rim; since the Hindhead Tunnel opened in 2011 the old road has been taken up and grassed over, and the walk round the Bowl to Gibbet Hill is quiet for the first time in two centuries.

Hindhead and the Devil's Punch Bowl

See Babbage's Difference Engine No. 2 and the Apollo 10 capsule at the Science Museum

Visit Michael Faraday's laboratory and the Faraday Museum at the Royal Institution on Albemarle Street, home of the Christmas Lectures

Visit the Alexander Fleming Laboratory Museum at St Mary's Hospital, Paddington, where he discovered penicillin in 1928

Visit the Old Operating Theatre Museum in Southwark, the operating theatre of 1822

At the Royal Institution on Albemarle Street, home of the Christmas Lectures, Michael Faraday's laboratory is kept as a museum. Alexander Fleming discovered penicillin in 1928 in his laboratory at St Mary's Hospital, Paddington, now a museum too. In Southwark the Old Operating Theatre of 1822 survives, and the Science Museum has Babbage's Difference Engine No. 2 and the Apollo 10 capsule.

Scientific London: Faraday, Fleming and the Old Operating Theatre

Stand under the Albert Memorial, opened by Queen Victoria in July 1872, and find the statue of the prince, seated in 1876

Find the Peter Pan statue by the Long Water, at the spot where Peter lands in Barrie's The Little White Bird

Go to Speakers' Corner in Hyde Park on a Sunday afternoon and listen to whoever is speaking

Go into the Palm House at Kew, built in 1844–1848, the first large-scale structural use of wrought iron

The Albert Memorial at the edge of Kensington Gardens was commissioned by Queen Victoria after Prince Albert died in 1861: George Gilbert Scott's canopy, 176 feet high and paid for by public subscription, opened in July 1872, and the statue of Albert was ceremonially 'seated' in it in 1876. Further in, by the Long Water, is the bronze Peter Pan of 1912, commissioned by J. M. Barrie himself and put at the spot where Peter lands in The Little White Bird after flying out of his nursery — Barrie lived just across the road on Bayswater Road. At the Marble Arch end of Hyde Park is Speakers' Corner, where anyone can turn up unannounced and talk about almost anything, at the risk of being heckled by the regulars; Marx, Lenin and Orwell all went. Upriver is Kew, founded in 1759 and now a World Heritage Site with the largest and most diverse botanical collections in the world, where the architect Decimus Burton and the ironmaker Richard Turner built the Palm House between 1844 and 1848 — the first large-scale structural use of wrought iron.

Kensington Gardens, Hyde Park and Kew: Albert, Peter Pan and the Palm House

Climb Butser Hill (271m), the highest point on the chalk ridge of the South Downs, and identify constellations above the escarpment

Walk the ancient yew forest of Kingley Vale National Nature Reserve by moonlight — some of Britain's oldest yew trees stand in this nature reserve north-west of Chichester

Photograph the Milky Way from the chalk ridge on a moonless night

The South Downs became an International Dark Sky Reserve, Moore's Reserve, in 2016. Butser Hill at 271m is the highest point on the chalk ridge of the South Downs, and the yew forest at Kingley Vale — some of the trees among the oldest living things in Britain — is a strange place to be at dusk.

Moore's Reserve: Butser Hill and Kingley Vale by Night

Taste the iron-rich water of the Chalybeate Spring on the Pantiles, discovered in 1606 by Dudley, Lord North

Stroll the Pantiles, the colonnaded Georgian promenade beside the spring

Tour Scotney Castle, the moated 14th-century castle and Picturesque garden, National Trust

Dudley, Lord North, found the iron-rich Chalybeate Spring in 1606, and the colonnaded Pantiles run beside it. Out in the Weald, Scotney Castle is a moated 14th-century castle set in a Picturesque garden.