The Nag’s Head is an establishment in Whitechapel that was a pub when Strike was a youth living in the area. Currently, it is a lap-dancing club.
When Strike encounters it on his reminiscent walk down the memory lane that is Whitechapel Road, he doesn’t go in, but not because he had any “objection to semiclad women gyrating around him while he enjoyed a pint, but he could not justify the exorbitant price of drinks in such an establishment, not when he had lost two clients in a single day.”
So he goes to Starbucks instead.
If you, however, are able and willing to go to the Nag’s Head, here it is on Google Maps.