The Upton Park outfit had been mired in a relegation fight but four consecutive wins have moved them into 10th place in the Premier League, seven points above the drop
Sam Allardyce's men have won four straight league games to move into the top half of the table and alleviate relegation fears at Upton Park.
West Ham have been plagued by injuries this term, with club-record signing Andy Carroll the most notable absentee for the majority of the campaign due to a heel injury, while both the former Liverpool striker and Kevin Nolan have also been out of contention through suspension.
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"It's very enjoyable at the club at the moment," Downing told the club's official website. "Everyone is back now from injury and suspension and that's what we've been waiting for.
"We've had a bit of luck along the way but I think we were due some. I'm happy personally because things are going quite well.
"The manager is obviously happy because the team is winning. The last couple of weeks it's all come together.
"We're not out of the woods yet because we've still got games to win, starting at Everton at the weekend."
Downing is anticipating a difficult match against an Everton side who have lost three of their last four Premier League matches, and he highlighted England international full-back Leighton Baines as a particular threat.
"Everton is always a difficult place to go, even when they're not playing that well," he added. "The crowd are really on top of you.
"Roberto Martinez is doing a good job there and his team is playing really well using a different way of playing to how Everton have (previously) played.
"I think Bainesy (Leighton Baines) has probably gone up a level the last couple of years, even though he was always a good player. In terms of creating and scoring goals, I think he has been one of the top players, so it'll be a good test."