Such a find would have either remained with the company and its successors (United Alkali Co merged into Imperial Chemical Industries in 1926) until donated to a museum, or may have remained with a senior company employee and may still be in private hands.
The patterns of company donations to museums can be haphazard and diffiult to predict. As the United Alkali Company had works in Liverpool, St.Helen's, Warrington, Glasgow, Widnes, Runcorn and Newcastle upon Tyne, the plaque might possibly have been donated to any of the municipal museums in these towns. After the merger into ICI the possibilites become more complex for whilst some objects such as this find might have been sent to the London headquarters and hence have been later donated to a London-based musuem, it might equally well have remained in one of the provinical offices listed above and been donated to a museum from there.
When works close, it often happens that interesting objects are appriopriated by employees. Objects such as this plaque might be retained by a manager or some other senior employee. If that person ultimately donated the object to a museum it might be at a location he retired to - which could be almost anywhere in the UK.
Vol.1 of W.J.Reader's "History of I.C.I" provides the fullest history of the United Alkali Co and hence might be a useful starting point to identify locations of works and hence possible museums the plaque migth have been donated to.