I have a metalic button 1.5cm with the gothic script of L&NW and GWR on it.Both railway co what is the link?

Question

I believe that london and northwestern railway were rivals with gwr, so why this button with both initials on.

Answer 1

London & North Western Railway - later part of the London, Midland & Scotland Railway (after 1923) The other is The Great Western Railway.

Maybe it was from a jointly-run part of the network (See Nostras answer).

Answer 2

The answer is the Birkenhead Joint Railway.  I didn't happen to find the dates of opperation, but the following information should help if you want to know more:

The Birkenhead Railway, jointly owned by the LNWR and Great Western, ran from Birkenhead (Woodside passenger station and Birkenhead docks) to Chester and from Chester to Acton Grange East Junction, on the LNWR main line south of Warrington, with a branch from Hooton to Helsby and a (single-line) branch from Hooton to West Kirby, where it connected with the Wirral Railway. From Acton Grange the Great Western had running powers to Manchester Exchange, for passengers, and Liverpool Road, for goods.