FlatsHome3 Stable Mews
John Steed lived at 3 Stable Mews at least between September 1966 and spring 1969.

It was Steed's flat during series 5 and 6 of The Avengers,

The flat is located near Portland Place/ New Cavendish Street, not far away from the BBC Broadcasting house, it's only a few minutes to Regent's Park and Oxford Street.
Go from Great Portland tube station to Park Regent, walk down the Great Portland Street until you see, New Cavendish Street on the right. Enter New Cavendish Street and after 70 meters you will see Duchess Mews to the left. Steed's flat is the last building (no.17) on the left site at the corner Duchesss Mews/ Duchesss Street

One could see the interior of the flat for the first time in the episode Escape in Time when Steed and Mrs Peel go from the mortuary to his new apartment.
In the series 6 episode Stay Tuned John Steed however says to the operator that he will be away for three weeks and that his phone number is: Whitehall 9819

According to the 3L 4N Director telephone system you would have to dial 944-9819 to call John Steed (Whitehall=WHI=944)

But in the episode My Wildest Dream Dr Reece tries to call Steed on a number that starts with 63...

Very odd to believe that Steed's - a secret agent - telephone number is in the book (From Venus with Love).
Furthermore the adress on his business card however is different from the one that can be seen on the envelope of George Unwin's invitation for John Steed in the episode You Have Just Been Murdered:
The house number is not "3", but "13" and the street's name looks like "Middle(ton)? Mews, Draw....(?), London.

Another address appears in Dead Man's Treasure, but it's not possible to read it.

The correct address however can be seen on the evelope containing the deadly virus in series' six epsiode "You Will Catch Your Death"
Just Have Just Been Murdered Dead Man's Treasure You Will Catch Your Death
His fourth flat in series 5 and 6 of The Avengers was supposed to be a building located at Duchess Mews SW1 in London, No. 17,City of Westminster.

What is the size of the flat? It has two floors with a living room, a storage room with Steed’s sport equipments as seen in Who’s Who???, a kitchen and a guest room. Upstairs there has to be the bedroom, bathroom and possibly a study.
17 Duchess Mews, London            -           3 Stable Mews in The Avengers
17 Duchess Mews London aka 3 Stable Mews, London in The Avengers       
Photos by Sinus from 2013
The backyard of the house on the right. There's definitely no second entrance to the flat in the 60s and today.
Photos from October 2013
Duchess Mews/ Stable Mews as it looks today
View from Duchess Mews to Duchess Street in the background.
Steed lives in the last house on the left site as seen in The Forget-Me-Knot.
Steed's house in 2013 (left) and 1968 (above). The front door and the former stable doors of the house are painted white today, but were originally black in 1968, the colour of the entrance door in The Forget-Me-Knot however is beige.
Steed's house front and house site towards Duchess Street in October 2013.
In 1968 the windows towards Duchess Street were bricked up.
Corner Portland pl/ New Cavendish Street New Cavendish street toward Duchess Mews Duchess Mews towards BT Duchess Mews towards Duchess Street BBC building
Steed's neigborhood
New Cavendish Street to Weymouth Mews Park Square to Portland Pl
Portland Place towards Oxford Street
John Steed's Flats - No.4
3 Stable Mews
3 Stable Mews, London
City of London

One can see the exact address and telephone number (490 -9618) on Steed's business card in series 6 Homicide and Old Lace.
It definitely says "City of London", so the location for 3 Stable Mews is not "City of Westminster".