Gripper, seconding what Harvey advised, give the solenoid a tap with a rubber hammer or something equally appropriate that won't damage the solenoid. My Rover's starter had the same issue, turn key, starter relay latching but no action from the starter. Whack the solenoid, sometimes more, sometimes less, try again and there she goes and we are on our way. This happened on and off, only very occasionally over the years until....last time it did it though, luckily in the garage for she wasn't going anywhere. I guess I tried for more than one hour all to no avail. I removed the starter and took it to an old school auto electrician. He did some fault finding, solenoid was not the problem, but there was problem within the armature, a number of shorts in fact where the protective coating had worn through. Parts that were not meant to be in contact were in contact. He retaped the problem areas, used a heat resistant araldite as an insulator and I paid the money. Once home, refitted, turned the key with anxious anticipation, and away she went! Problem fixed.
The moral of the story being, although it may be the solenoid sticking, at the end of the day it may not be, and if it isn't, the problem is possibly not in the solenoid at all, but somewhere else.
Ron