Adam, whose Upton Park contract runs out this summer, will be able to put himself in the shop window, although a permanent transfer to anyone but the O's would not be possible this campaign as his month takes him beyond the transfer deadline.
He links up with former Hammer Paul Brush, manager of England's 90th placed team in the third division, though the danger of relegation is a distant one.
Adam was man of the match in the 1999 FA Youth Cup final over Coventry City - the side against whom, incidentally, he made his full debut in September 1999 - but has found it difficult to follow contemporaries like Joe Cole and Michael Carrick into the first team.
His last loan spell was at Notts County, when Peter Storrie was there, and he has also been at Portsmouth - where Peter is now.