Sam Allardyce's side are now looking over their shoulder after a poor March that has seen them lose all of their Premier League fixtures.
Four wins in as many matches in February looked to have pushed West Ham towards survival, but since the turn of the month they have struggled, following defeats at Everton and Stoke City with a 2-0 home loss to Manchester United on Saturday.
West Ham now sit 14th in the table - just six points above the relegation zone - and were overtaken by Hull at the weekend by virtue of Steve Bruce's side's 2-0 win over West Brom.
"It is going to be tough. We've still got eight games left and we've got to put some points on the board," West Ham midfielder Mark Noble told the club's official website.
"Obviously it (is) a big game on Wednesday. Hull beat West Brom on Saturday so they are going to have confidence, but we need to play like we can do at home."
West Ham could perhaps feel hard done by on Saturday - Wayne Rooney scored an outrageous goal from distance before pouncing on a miscued Noble clearance to net the second - but they failed to cause any real problems for a makeshift United defence.
Allardyce will demand more of striker Andy Carroll against a Hull side that have the sixth-best defence in the league.
Goals from Liam Rosenior and Shane Long gave Hull their victory over West Brom, taking them to nine Premier League wins for the season.
And manager Bruce believes one more triumph may be enough for the club to secure their position in next season's top flight.
Bruce told Hull's official website: "I've said all along that I thought 10 wins would be enough.
"Whatever it takes, we have to see it through but if we can get to ten wins with seven or eight games to play it means other teams have got to maybe win four and draw a couple which is very difficult."
The 12th-placed Hull - who have one eye on their FA Cup semi-final against Sheffield United next month - could be without Long, who suffered a knee injury on Saturday.
George Boyd remains suspended after being found guilty of spitting at Manchester City goalkeeper Joe Hart, while Robbie Brady (groin) and Paul McShane (ankle) are long-term absentees.
Defender Joey O'Brien (dislocated shoulder) and striker Marco Borriello (calf) are set to miss out for the hosts.
Brady scored the only goal in Hull's 1-0 win in September's meeting between the two sides - just the fifth occasion they have met in Premier League history. West Ham and Hull have both won two of those clashes.
