The main focus of this hand coloured engraving is the Old Bath Hotel, with the grounds of the Temple Hotel in the foreground. On this particular image, unfortunately, it isn't easy to distinguish the oval stone commemorating the Old Bath's rebuilding by Smith & Pennel's son in law, Stephen Egginton, but it can be seen on the previous image.

The Temple and the Old Bath had been under joint ownership and it was The Temple where Lord Byron stayed when he was attempting to woo Mary Chaworth; she stayed in the more sumptuous surroundings of main building of The Old Bath^[1]. In 1799, so eleven years or more before this engraving, the then proprietor John Leedham announced that he had made improvements to the hotel^[a]. A year later he placed the following notice in the Derby paper announcing more improvements:

However, in late 1806 the Old Bath and the Temple were advertised as being to let, either separately or together^[2], and John Leedham moved to The Hotel (Museum Parade today) in the early spring of 1807^[3]. Joseph Notzel Cumming became the proprietor of the Old Bath^[4] and Eneas Evans took over at the Temple^[5]. In his 1818 "Picturesque Excursions" guide, Henry Moore described the Old Bath as having "a spacious carriage drive, which partly encompasses the garden in its front", which we can see in this engraving, and it was "continued [as] a terrace walk to the Temple, a sweetly situated lodging house, kept by Mrs. Evans".

After visiting Matlock Bath about 1824 Ebenezer Rhodes described, in his book "Peak Scenery"^[7], the three inns that were in Matlock Bath at the time as excellent. He wrote:
"The principal one [hotel] is denominated the Old Bath, and it is a spacious building capable of affording accommodations to nearly one hundred visitors. At this inn there is an excellent assembly room, lighted with elegant glass chandeliers; and a hot and cold bath are included within the establishment".
... In addition to the inns, there are many comfortable lodging houses, the principal of which is kept by a Mrs. Evans, and known by the name of the Temple. ... It is connected to the Old Bath by a spacious terrace carried along the side of the hill, which forms a most delightful promenade".

Of the evening entertainment provided he wrote "we returned to the village of Matlock ... on our arrival we found the promenades deserted; the lights were glimmering through the trees, and the musicians at the Old Bath were tuning their instruments for the evening's assembly".

References (coloured links go to on site transcripts):

^[1] Various biographies of Lord George Byron mention this and J. B. Firth - (1908) "Highways and Byways in Derbyshire", MacMillan & Co., London - also discusses the romance at some length.

^[a] "The Derby Mercury", 4 July 1799. Leedham's advertisement, stating he had made alterations and improvements, was dated 21st June, 1799.

^[2] "The Derby Mercury", Thursday, 11 September, 1806 (and other issues). See a transcript of the announcement on Matlock Bath, 1806

^[3] Matlock and Matlock Bath: Public Notices and Announcements, 1807. John Leedham was already in financial difficulties in the latter months of his time at the Old Bath. These continued for a few years. See: See Matlock & Matlock Bath Names in the London Gazette, 1801-10 between 1806-10 and 1811

^[4] "The Derby Mercury", Thursday, February 12, 1807.

^[5] "The Derby Mercury", Thursday, 19 March, 1807.

^[6] See "Picturesque Excursions From Derby to Matlock Bath"

^[7] Rhodes, Ebenezer (1824) "Peak Scenery" pub. London, Longman, Hurst, Rees, Orme, Brown, and Green, Paternoster Row.