There were still a lot of sailing ships around in 1907 so this squarerigger is probably nothing out of the ordinary. There are frequently photos of sailing ships of the period in Dover available on Ebay but they tend to be a bit pricey.
As regards HMS Illustrious, the photo is annotated as showing her on a voyage from Portsmouth to Plymouth, presumably doing an anti-clockwise showing-the-flag trip around the UK. This was in 1983, the year after the Falklands, so may have something to do with it. Illustrious was rushed into service and went down to relieve HMS Invincible after the war ended.
Illustrious paid another visit to Dover a few years ago. I recall that not many of their matelots were to be seen in the pubs of Dover which is certainly a change from the old days. Here is a sketch entitled "Neutrality" made in a hostelry in Dover in 1877 showing sailors and soldiers competing for the attention of the serving wench, probably just before all-out hostilities commenced!
Full size version available here:
http://shipsintheportofdover.fotopic.net/p64606360.html