"One of the most extraordinary old houses in London was one sketched by J. T. Smith, in 1792, and taken down in 1801. It stood at the end of a low dark court on the south side of Hart Street, and was universally known in Crutched Friars as Whittington's Palace. The last lodger was a carpenter, who had sunk a saw-pit at the north end of the courtyard. The whole front of the house, which had originally formed three sides of a square, was of carved oak. The tradition was that the cats' heads carved on the ceilings always had their eyes directed on the spectator wherever he stood, and that even the knockers had once been shaped like cats' heads. Two sides of the outer square were nearly all glass lattice, and above and below ran wild-beasts' heads and crouched goblins, that acted as corbels. The doorway panels were richly carved, and above and below each tier of windows were strings of carved shields, including several arms of the City companies. "

Old and New London: Volume 2. Originally published by Cassell, Petter & Galpin, London, 1878.

But contemporary accounts suggest this isn't Whittington's Palace, e.g.:

"Whittington’s House, or Palace

Hart-Street, Crutched Friars, contained the remains of an old building, which has long been termed Whittington’s Palace, and is so called in the leases of the premises. The site may have been originally that of his dwelling; but the present building certainly never witnessed the days of the worthy mayor; in short, it is evidently of the ridiculous style prevailing since the time of Henry VIII.; a stupid mixture of heterogeneous ornaments; the shields, on a sort of frieze between the ground and the first floors, are separated by brackets and distorted caryatides, and contain the arms of several companies; besides the windows are of the true Elizabethan angular shape."