The Hammers were flying high in the Premier League at Christmas last year, but they suffered a spectacular collapse in the final months of the 2014-15 campaign.
Sam Allardyce was the manager at the time, and under him West Ham ended up 12th in the league table.
West Ham are going strong at the moment under Slaven Bilic, and Brady seems confident that the side will continue to pick up points.
“Slaven Bilic urges caution, supporters shouldn’t raise their hopes too high,” the West Ham vice-chairman wrote in her football diary in The Sun (Saturday, September 26 entry).
“Although the signs of a promising new era are all around us at West Ham, a year ago there were similar feel-good emotions only for momentum to disappear amid a sprawl of injuries, lost points and eventually the manager’s job, too.
“Our spirit remains strong today and we equalise in injury time against Norwich. This is a strong team and I believe we are going places.”
West Ham are third in the Premier League table at the moment, but one suspects that they are unlikely to retain that position as the season progresses.
A top-eight finish is what the London outfit are aiming for this campaign, but they could end up in the top six.