The house where Pitt stayed at Bath
The biographies say that in 1802, Pitt stayed at a house on Pulteney St. (more properly Great Pulteney St.), a long, wide thoroughfare running from Pulteney Bridge to Sydney Gardens. The exact house is not recorded. Later, for his final visit in 1805, he is said to have stayed at 2 Johnson (or Johnstone) St. The two houses were not far apart - Johnstone St. runs off Great Pulteney St. via Laura Place - but it seems certain they were two different houses.
The commemorative plaque, which says Here lived William Pitt, A.D. 1802, is on no.15 Johnstone St. In all probability, this was actually no.2 at the time, and it has since been renumbered. On the detail from an 1803 map of Bath, the red dot shows the location of today’s no.15, and you can see that the rest of the street had not yet been built up. It’s a reasonable assumption that the house was renumbered at some point after the street was subsequently developed.
The bottom picture is from Google Street view, and shows more clearly the position of the house (on the left) in relation to Laura Place, just round the corner to the right.
Now, as to the date on the plaque - I think it must be wrong. This must surely be the house he stayed at from around mid-December 1805 until early January 1806. The only way it can be the 1802 house is if, as Johnson St. was still undeveloped, the address of this house was given as Pulteney St. instead. That wouldn’t be unreasonable, since it’s only just off the main road. But in that case, where was the 1805 house? Johnson St. may well have had more houses on it by 1805, but which one would have been no.2, if not this one?
Of course, all of this assumes that Pitt’s biographers have got these trivial (but to me highly important!) details correct…