Trendified pubs full of bearded hipsters braying loudly while taking selfies, what’s not to like? 
The Guardian’s Lifestyle (ghastly word) section is generally to be avoided at all costs, or dipped into only after partaking of a decent quantity of Old Peculier or Young’s Special.
The Viaduct Tavern is a good place. It is often glimpsed on news reports because it is just across the road from the Old Bailey
I might have been in there as my usual hotel in London is the Strand Palace just down the road, and when younger and dafter I was prone to crawling from Strand to the bottom of Fleet Street and back. Ye Olde Cheshire Cheese is the only pub name I can recall.