I had a quick Google and discovered that Rosehill House, Derby is Grade II listed, and I may have found some info about the architect. It may have been designed by Edward Buckton Lamb -
https://historicengland.org.uk/listing/the-list/list-entry/1396602?section=official-list-entry
Rosehill House, possibly designed by E. B. Lamb around the 1840s, is designated at Grade II for the following principal reasons: * Architectural interest: for the high quality of its imaginative Tudor/ Jacobean style design and the very possibly designed by the nationally important architect, Edward Buckton Lamb. * Materials: the materials used are of the highest quality available on a large scale in the 1840s, such as the Staffordshire brick and slates. * Survival: the plan has remained virtually unaltered and many of its original fittings survive, giving a good impression of the appointments expected of an early Victorian industrialist. * Group value: it is one of the first buildings associated with the Grade II* Registered Derby Arboretum, designed by J. C. Loudon 1839-40, with entrance lodges and shelters by E. B. Lamb.
Also -
https://her.derbyshire.gov.uk/Monument/MDR11462
The house is a pretty Neo-Elizabethan villa, built in the 1830s for John Bingham, possibly a rebuild of an earlier villa. Built of brick, diapered with blue Staffordshire bricks, it has stone dressings, including mullioned and transomed windows, and quoins. It is of two tallish storeys and attics, embellished with straight coped gables, and has tall Tudor-style chimneys. (1) A grade II listed Tudor and Jacobean revival-style house, possibly designed by E B Lamb around the 1840s, with late 19th century alterations and a small early 20th century extension. The house is constructed of red brick laid in Flemish bond, decorated with diapering of Staffordshire blue brick, with sandstone dressings, under gabled roofs clad with alternating courses of Staffordshire blue plain tiles and fish-scale tiles. The house has two storeys plus attic and is situated on a corner plot fronting Wilfred Street to the west and Rose Hill Street to the north. It has an asymmetrical plan consisting of two parallel ranges running north-south, each with a central projection under gabled roofs. The west projection is the three-storey entrance porch and that to the east is a two-storey domestic projection housing the housekeeper's room on the ground floor. The service rooms were sited to the north leaving the main reception rooms facing south. Rose Hill House is situated opposite the Arboretum, which was established in 1839-40. The entrance lodges for the Arboretum were built by Edward Buckton Lamb, a nationally important architect, whose imaginative neo-Gothic and Tudor revival designs are stylistically similar to Rose Hill House. There is no direct evidence for Lamb's involvement in the design of Rose Hill House; however there is good reason to suppose an association. See List description for more details. (2)
In terms of the conservatory, your best bet may be to scrutinise the glazing bars and columns to see if there are casting marks/ stamps which identify the foundry which made the conservatory. If the house had been on the east coast of Scotland, I would have suggested Mackenzie & Moncur in Edinburgh as a first port of call, they were iron founders and built lots of conservatories and glasshouses using cast iron components as a "kit of parts". They're still in business -
https://www.mackenzieandmoncur.co.uk
However, as there were lots of iron foundries around the Derby area, eg. Leys, it's likely to have been supplied by a local firm. Also just to flag that J.C. Loudon is John Loudon, who was a very famous Scottish landscape designer who wrote several books about landscaping and horticulture - if he was involved with the arboretum, potentially he may have been involved with the conservatory, too. From experience of Victorian-era conservatories, the timber work was probably Oregon Pine (Douglas Fir), but don't quote me!
Suggestion would be to contact the Conservation Officer in the Planning Department at Derby City Council and ask to see any information they hold about the property. They may charge a fee to carry out a search, but should be able to tell you about any documents and drawings they have in the archives.
Good luck.
