Hi Anna
The short answer is - no. I’ve had a look at it. You won’t find it helps.
I expect you will find some more recent books published about Redditch with info about your Milward and Bartleet families, but here are two that do have some information, albeit more from the business perspective:-
1) “The Personal Reminiscences of a Needlemaker by Bernard T Lee. Published by Merlin Books Ltd, Braunton, Devon in 1986. ISBN 0 86303 311-3
A quick look at the book. It is essentially a full history of Henry Milward & Sons, and includes in its early chapters( up to page 33) information about the 18th and 19th century history of the trade, Redditch factories before 1930 and their amalgamations. By 1986 the company was known as Needle Industries Group Ltd
and
2) A History of Redditch by John G Rollins. Published by Phillimore in 1984 ISBN 0 85033 515 9.
I think you nedd to take a holiday in the Midlands! If you have a look at The National Archives (TNA) website and do an advanced search for Milward and Redditch, you will find there are many potentially fascinating documents, lithographs, photos and booklets etc which relate to the Milward family and Needle Industries and Associated Companies, which are held at the Warwickshire County Record Office (including a booklet written by a Bartleet about the Needle trade). There is also a collection at the Worcestershire RO. Full details of which are not on the National Archives website. As I recall it includes some personal letters.
The National Archives website has under "Exhibitions" an on-line drawing showing an 1870 Henry Milward & Sons design for a needle case. Bernard Lees book cover has been designed using a colourful variety of needle cases mainly Milwards, but also Halls and Bartleets and others.
For info on St Stephens Church Redditch and the Bartleet fountain navigate around the following website
myweb.tiscali.co.uk/webbsredditch
HTH
Nemo