explores the use of terms like "manufactured for". Your focus should be that this is a John Brinsmead piano - a famous maker. Inside the top, you should find some numbers, which may enable me to date it, but what I would like to see is photos that show what the WHOLE piano looks like.
Manufacured for Robert Cross & Son eccles ..on my mothers piano
you will see that there were thousands of similar pianos made in the first decade of the 1900s, and Brinsmeads were not usually different in any obvious way to the others, apart from occasional special designs. If you want to search inside the piano for clues, have a look at