I was going to suggest Islington!!
Also, things are unlikely to get stolen in Trafalgar square. Its so busy, and there is always police around, theres no way you would get away with it. As for the pigeons they went in ahout 2004, so if you're writing before then, they would still be there.
With somewhere to work, I'm not sure about the medicine thing, as anything with medicine would make him like a doctor... but you said buisness man. Big buisness areas could be somewhere like canary wharf.