I have ImageMagick installed and this, plus the Imagick extension, was working fine in PHP 5.6. Currently using the PHP 7 nightly build on Ubuntu 14.04, installed as per: http://php7.zend.com/
I understand there are compatibility issues, so I have found this https://github.com/mkoppanen/imagick/tree/phpseven and have attempted to install it, basically with:
OK, so I did make some pretty basic mistakes here, though hopefully not obscure enough that the eventual solution won't help some people in the future.
The first issue was that I was indeed running phpize from PHP 5 - I thought I had symlinked this properly but I hadn't.
So aside from that, he first command to run was:
My second mistake was that ./configure also assumed I was running PHP 5, so to correct this I had to run:
make install worked and copied the files to the correct location automatically.
Thank you @Danack for your comments, they helped!