Yes, the machine is Rex, identifiable by the front axle sliding between the parallel tubes. According to Jamie Dee (writing in "Old Bike" No 9, Spring 1994 - try eBay if you don't have the 32 issues, packed with still-useful stuff), this fork was replaced in 1909, so I suspect this one is 1907 or 1908. The difference between the two is that for 1908 the saddle height was lowered by dropping the top frame tube. Now I fancy I can glimpse the rear stays heading up to join the top tube somewhere in front of the saddle position, so maybe 1908. If that lad would just step to one side...
The bike seems to be the 3 1/2 h.p. (500 cc) single: there was also a V-twin.
Leon