Put simply, the C-17 was considered too big and too expensive to be a candidate for the FLA programme.
The RAF later leased it as the STSA, pending ultimate delivery of a larger number of A400M aircraft. Which do not have the same ultimate capability as the C-17A, but will be acquired in substantially larger numbers.
The STSA was a prudent move, given Bliar's susbequent interventionist policy in Iraq and Afghanistan.
The payload range characteristics of the A400M have been agreed to a European requirement which did not exist '25 years ago'. You may as well bring HS681 into the discussion, if you insist on bringing ancient history into the issue.
I well recall my first experience in looking at the potential of 'Solution 10' of the 'FLA' in 1994 (for DFS as it then was) as a tanker. The design was far from frozen then; indeed, it has only been frozen in the last few years. Since then, the programme has proceded without major issues.
Back to the Euroheavychopper, the Mi 26 would be unlikely to be more expensive. Of course, had C-17A been offered for sale at a price less than that of the A400M, it would have been rather daft to continue with the programme.
I don't see the need for Euroheavychopper; whereas the A400M is to be less expensive than the ('too big, too expensive') ultimately more capable C-17, I cannot see that being true for the Euroheavychopper.