I was watching Peaky Blinders and in one episode John and Arthur went to catch one old guy and lady. Lady was john and Arthur's teacher. On that time they were standing near Titanic. What is the purpose to show Titanic ship?
Sounds like it could be a mistake
From the TV Tropes page on Peaky Blinders:
Artistic License – Ships: Season 3, episode 3 features a brief shot of a Cunard Line ship docked in Liverpool. Likely meant to be the RMS Mauritania, the CGI model appears to be the hull and superstructure of the RMS Titanic with the vents, forecastle, and colors of the Mauritania added.