How do I change permanently the encoding of a text file?

Question

I have a bunch of html files encoded as iso-8859-1-unix and a few encoded in utf-8-unix. What I want is to encode all of them in utf-8-unix. I have already tried (I think they are the same command, actually):

C-x C-m f utf-8-unix
C-x RET f utf-8-unix

the modeline changes from 1 to U, but after I close the file and reopen it, the modeline shows 1 again. It seems that I cannot make the change permanent no matter what I try and I don't understand why.

Following the suggestions below, I have created a new file with this content

<ul class="navbar">
  <li><a href="index.php">home</a></li>
  <li><a href="bio.php">bio</a></li>
  <li><a href="research.php">research</a></li>
  <li><a href="software.php">software</a></li>
  <li><a href="contacts.php">contacts</a></li>
</ul>

C-h v buffer-file-coding-system returns this:

Its value is utf-8-unix
Local in buffer new.htm; global value is the same.

so it looks okay. I save, kill the buffer, reopen the file and C-h v buffer-file-coding-system returns this:

Its value is undecided-unix
Local in buffer new.htm; global value is utf-8-unix

I am really confused.

EDIT: thanks everybody for helping making this clear!

Answer 1

N.B.: Question answered in comments.

Answer 2

using M-x add-file-local-variable RET coding RET utf-8 RET did not work for me. What did was to add this to the topmost line, as e.g.

# -*- coding: utf-8; -*-

(org-mode comment is #)