A book of piano serial numbers is called a Piano Atlas and is used to look up the date of a piano's manufacture. This page is at best, only a mini-atlas but is still a useful reference point. An exact date does not really make any material difference to an assessment but to be within 2 to 5 years is accurate enough to give an informed report on a piano.
Occasionally the name on the piano is not the manufacturer but simply a transfer name. In these cases the serial numbers will mean nothing at all.
Experience will help to estimate the age of a piano with no name or with no serial number. The action, the key covering, the style of the casework - all give clues to its age. An educated guess will narrow down the age of a piano to within 10 years or so.
The serial numbers for the piano makers listed below are mostly from 1920 to 2000. There are occasional irregular intervals especially during the early 1940s - the WW2 period - when very few pianos were built in Europe.
Barrett & Robinson
Collard & Collard
Duck, Son & Pinker
Gors and Kallman
Ivers & Pond
Marshall & Rose
Monington & Weston
The source for most of these numbers is of course the far more comprehensive Pierce's Piano Atlas. The format for each maker is in the form of a simple table.