You are not going to find any more info on Thatcher than this document: https://sha.org/bottle/pdffiles/ThatcherFirms.pdf
The 4 could be a Plant code, 45 possibly a date code.
Understand that Thatcher (or any glass manufacturer for that matter) made bottles for hundreds if not thousands of clients. Research on 20th century glass manufacturers as well as bottling companies is by no means complete....this is the work of painstaking research by just a few people in the US. I would direct you to the bibliography in the above referenced link if you want to dig deeper.