will all hdmi cables work at 1080p at a length of 10 metres?
Not all of them.
With a cheapy cable the only way you will know is to test it yourself with your own AV kit.
Some people have problems with cheapy long cables, especially near mains cables or if the cable has many bends around corners etc.
Cheapest manufacturers are cutting each others throats to produce cheaper and cheaper HDMI cables, and the quality is suffering with some of them for sure.
Post #3 by nwgarratt in this thread
http://www.avforums.com/forums/showthread.php?t=597408 mentions some cables he tested that would not work at 720P. Must have been untested cables he bought.
Also a cable that works when laid across the floor when you test it, might not work when you install it under the floor or in the ceiling near power cables.
Some quality cables can easily be run 10 metres at 1080P with mains cables parallel to them, I know I have tried lots of them
(We test every cable at 1080P before despatch)
Mark.