A bit off topic,(there is a BSA M21 in the picture),looked on the www and cant find any info on this dealer,the tele fork BSA might give a clue ,middle forties onwards at a guess or early fifties.
Looks as if they were based in East Dulwich. Using Google and entering 'pullins motorcycles east dulwich' you should get a number of hits. As always these searches are good fun and often reveal an interesting lost history.
The original building still stands, found it on Google Street maps,its 74 Lordship Lane East Dulwich, building now in use as a Japanese restaurant,the building to the left of it is a dry cleaners,many of the original features still remain.
For amusement take a look at the building to the right, a bank. Then move along the street just beyond the bank, turn around to look back at Pullins (now the restaurant) and you'll see that the bank transforms into Screwfix - magic!