On Monday May 11, 1612, “one Mr Shakespeare”, as a witness put it, entered the Court of Requests at Westminster and, at the end of his testimony, signed a deposition. His is a scrawled signature that, as Charles Nicholl suggests in The Lodger: Shakespeare on Silver Street, might indicate impatience; or simply the quickness and fluency of his hand.

The case itself was not notable for comedy or for tragedy; it was a domestic drama of the commonest kind. Stephen Bellott was suing his father-in-law, Christopher Mountjoy, for full payment of a dowry; both were French, residing in London, with Bellott an apprentice to Mountjoy in the business of “tire-making”, the manufacture of ornamental head-dresses so popular in the Elizabethan and early Jacobean period.

Shakespeare had been the lodger of the Mountjoys, living above the shop, during the courtship and wedding of Bellott and Mountjoy's daughter Marie. Indeed it seems that he was the mediator in negotiations immediately preceding the marriage. One witness suggested that the playwright formally betrothed the couple in the ceremony known as “hand-fasting”. So he was obliged to appear in court to testify to the financial arrangements. It could not have been a happy experience. The only public pronouncements that he enjoyed were made on stage.

Nicholl proves himself once more to be an expert investigator, with an enviable ability to hit upon the local detail that can illuminate a whole aspect of the world. He is at home among what he calls “parish registers, subsidy rolls, probate records and medical casebooks”; but it is only through such rigorous and impassioned attention that we can hear the voices of the participants in this story. They might be in the next room.

He gets tantalisingly close to the lives of those he investigates, tracing their names in obscure or forgotten documents, conjuring out of the briefest reference a story and a fate in what he calls “a world of aspiration and contact-mongering, a world of amorous and commercial rendezvous”.

Shakespeare walks here, too. He was the footstep on the stair, the familiar figure opening and closing the door. He was 40 when he joined the family in Silver Street, an official “gentleman” with his own heraldic device, but also a player of uncertain reputation. He was a man of property, but chose to live as a lodger in London. He was “friendly”, witty and unassuming in company; but in the shadow world of his plays he impersonated madness and savagery. As always, he is elusive and ambiguous. There is no way anyone can get close to him. If this is true of his biographers, it may also have been true of his contemporaries.

His presence in Silver Street is interesting. It seems that he liked living with what were termed “strangers” — more precisely, the French. In his plays, as Nicholl points out, he depicts a “rose-tinted France of the imagination, where love wrangles with philosophy”. His role as a lodger also emphasises that sense of belonging and not belonging that follows him everywhere.

One of his acquaintances was George Wilkins. Shakespeare collaborated with him on Pericles, but Wilkins was not simply a part-time hack playwright (Shakespeare was not fastidious in such matters); he was also a tavern owner and brothel-keeper, a violent and dangerous man with a habit of beating up the women he employed. He wrote a play for Shakespeare's company, The Miseries of Enforced Marriage, and became the landlord of Bellott and Marie Mountjoy after Shakespeare had helped to arrange their marriage. He was also a thief and receiver of stolen goods. He is one of those representatives of lowlife that are so colourful in the pamphlets of Nash and of Greene, but who must have been less prepossessing on the real London streets. His tavern was on the corner of Cow Cross and Turnmill Street, where a public house still stands.

This man's acquaintance with Shakespeare was not as unnatural as it might seem. Prostitution and playwriting went well enough together; the theatres were notorious “pick-up” areas. Wilkins also represents a world that Shakespeare depicted in Measure for Measure, in which the “lowlife” scenes reek of London in 1604. The brothel scenes in Pericles are also pertinent. Nicholl goes so far as to identify “Silver Street plays”, including All's Well That Ends Well and King Lear, that are redolent with the milieu. When Shakespeare described brothels and pimps, he knew of what he wrote. There were anecdotes concerning his lubriciousness, and there is little reason to doubt that he took full advantage of the looseness of the theatrical demi-monde.

This is the world Nicholl reproduces in an account that is as interesting as it is intricate. He has brought to life an aspect of Shakespeare's career that has been less exhaustively studied than most, and for that reason alone his book is worthy of praise. But he also casts a bright light upon the narrow streets and houses of early 17th-century London; you could not hope for a more expert, or more exact, topographer. The detail is delicious. It is almost prodigal. Nicholl is not so much a biographer as a detective. The Lodger is a triumph of reconstruction.

The Lodger: Shakespeare on Silver Street by Charles Nicholl

Allen Lane, £20; 400pp

Times Recommends

• Why do Pynchon, Ballard and Wallace provoke such online loyalty?
• The Sunday Times 100 best holiday reads
• What will we be reading this summer: the booksellers predict