This is a fairly difficult to trace alley that seems to be ancient heritage, but is probably quite modern.
The area around Lewisham Street started to be built up in the medieval period, as Westminster Abbey and Whitehall Palace became established.
The area of this alley follows the line of a path that passes through the middle of fields, and can be seen in a 1658 map by Faithorne and Newcourt, but the area was built up and the route lost for several hundred years. Lewisham Street emerged along that ancient path line back in the 18th century when the area was rebuilt. The alignment is however almost certainly coincidental.
Initially known as St John’s Street (John Strype 1720), it was split into two and was renamed Dartmouth Row along the Western half, and Lewisham Street on the Eastern half (Richard Harwood 1792).
This appears to be due to a local resident and politician, the Earl of Dartmouth who was, and indeed, still is also Viscount Lewisham.
By 1894 the entire alley was known as Lewisham Street (OS 1894), presumably to differentiate it from the nearby Dartmouth Street.
The area was initially built up with smaller terraced housing built largely rebuilt in the grander Victorian style as Empire encouraged institutions to set up shop near to government. Although the alley suffered damage during WW2, it was modest, and most of the changes since then have been modern redevelopments.
The unusual name for the pub comes from men who used to carry sedan chairs for the well-to-do people of London in the 18th century. Situated opposite the pub was a theatre called the Royal Cockpit where the upper classes would bet on cock fights. The men carrying the sedan chairs would for their next fares in the pub, hence the name The Two Chairmen
The rest of the alley, which was once a road but long since been pedestrianised is fairly routine frankly. A building site seems to have been here for years as I have never managed to take a photo of the alley without it.
A few of the buildings have some interesting detailing, but essentially, this alley is the back entrance to a lot of buildings with far grander front doors. Despite that, it’s a clean, wide and convenient route through this part of Westminster.
Especially if wanting to visit the pub.