Still no luck despite trying all the above. I have a couple of days of photos missing from two weeks of holiday pics. Very frustrating. Good to know I'm not alone but..... I am adding this comment a few hours later. The photos finally synched. I am very happy! Thanks for all the good advice.
I tried turning off my phone and laptop whilst it was still plugged in and also tried unplugging my phone and putting it back in. To no avail.
I turned off iCloud Photo Library which saves all images to iCloud automatically to save space on the phone. It deletes your current items saved with iCloud (would be all images on the phone) so try and share them on your device using iCloud Photo Sharing and save them to your iPhotos.
Turn off iCloud Photo Library on your phone and when you plug your phone into your computer it will load all images saved on the phone.
I had this problem, but found that the solution was not complex. The key to doing this is that your iPhone should be visible under "Devices" when you open "Photos." If this is not the case, use a USB connection and try the usual such as turning applications off and on. Once you see the iPhone from which you wish to import photos and videos under "Devices" in the menu on the left of the screen, click on that phone, and then go to Import... The rest should be self-explanatory.