Chatham Central Station wasn't really that Central to Chatham.It was in a part of Chatham called "Chatham Intra"(which was a small Area between Gundolph Road,Chatham and the Railway viaduct over the High street between Rochester and Chatham.
South Eastern Railway(SER) had linked London to strood by 1849 and London,Chatham and Dover Railway(LCDR..formerly East Kent Railway) which was a rival railway to SER,linked East Kent to Chatham by 1858 and then carrying passengers for London via a Horse Bus to Strood station.
Then the LCDR extended its line to London Victoria,leaving SER stuck at Strood.so it built it's own section of Railway between Strood and Chatham.(including its own Railway Bridge over the River Medway)
LCDR built a goods yard to obstruct and slow down the SER line,so they had to build a viaduct over it.
The new SER line had a Station at Rochester called Rochester Common and then later they continued the Line to the very edge of Chatham to Chatham Cental Station which was opened in March 1892.
The duplication of lines and Stations were a drain on both companies so they merged in 1899 making the South Eastern and Chatham Railway.
Chatham Cental station was now virtually obsolete.it was finally closed in 1911 and then later demolished.
Rochester Bridge Station was built when the LCDR extended it's East Kent line from Chatham to London Victoria in 1860.
The Station was rebuilt in 1908.However,It closed on 1st January 1917 as a Wartime economy measure and then eventually demolished in 1968 with great difficulty due to the solid Yorkshire stone used in its construction.
New Brompton station was opened by the East Kent Railway in 1858.The Name boards at the Station proclaimed "New Brompton,an area of Gillingham".The station was further along the line from where Gillingham station is today.The entrance was opposite Kingswood Road.
When the South Eastern and Chatham Railway came into being it changed it's name to "Gillingham"Station.
In 1890 the Victoria Roadbridge over the railway lines was opened.Then in about 1911 the 3rd Platform was added.The present day Gillingham Station building was opened in 1932.