The phrase everyone wants is the phrase almost nobody wins
'Web design London', 'plumber London', 'accountant London' — the broad service-plus-city phrase feels like the prize, so it is where most businesses aim their whole effort. The problem is that it is the single most contested phrase in their market, defended by competitors with years of domain age and hundreds of backlinks. A newer or smaller business pouring its budget into that one term typically spends months and ranks nowhere.
Meanwhile the searches that actually convert sit just beneath it, far less contested, and are ignored. The mistake is treating the head term as the goal rather than as the hardest, last thing you earn — after you have built authority on everything around it. Aiming there first is the most common reason a technically fine London website produces no enquiries.