They have beaten the likes of Arsenal, Liverpool and Manchester City - all away from home.
But despite having a number of Englishmen in their first team, including Carl Jenkinson, James Tomkins, Andy Carroll, Cresswell and Noble, not one has been included in Hodgson's squad for their Euro 2016 qualifiers against Lithuania and Estonia.
That is despite Hodgson's men having already qualified for the tournament and plumping for the surprise inclusion of teenager Dele Alli - who has started just one game in the Premier League for West Ham's fierce rivals Tottenham Hotspur.
'Surely it is time to give Hammers duo a chance?'
And now former Hammers favourite Sinclair - who scored 35 goals in 177 appearances during his five years in East London, making it into England's 2002 World Cup squad in the process - says Hodgson has missed a trick by omitting the likes of Noble and Cresswell.
Posing the question to the club's fans and football writer Henry Winter on Twitter, Sinclair said: "West Ham fans must agree surely it's a perfect time for England to have a look at Mark Noble and Aaron Cresswell Henry?"
Hodgson's West Ham blind spot
Noble was recently named West Ham's new captain while Cresswell has appeared, and shone for the most part, in every Premier League match since signing from Ipswich Town in the summer of 2014.
Given the fact England have already secured a safe passage to next year's finals, many Hammers fans felt at least some of their players would receive what they feel is long overdue international recognition.
But Hodgson has ignored them once again, with his inclusion of Alli a real slap in the face for Noble in particular.
West Ham and England have always enjoyed a special relationship. Indeed, whenever England play away matches, West Ham fans have historically made up a large section of the support.
Hammers fans' patience has been well and truly tested by Hodgson, though, who since taking over has been reluctant to include players plying their trade in the famous claret and blue.
The 68-year-old has been in charge since 2012 and since that time has only ever called up two players from West Ham - Carroll and Stewart Downing.