How to fix height of TR?

Try putting the height into one of the cells, like this:

<table class="tableContainer" cellspacing="10px">
 <tr>
  <td style="height:15px;">NHS Number</td>
  <td>&#160;</td>

Note however, that you won't be able to make the cell smaller than the content requires it to be. In that case you would have to make the text smaller first.

Tables are iffy (at least, in IE) when it comes to fixing heights and not wrapping text. I think you'll find that the only solution is to put the text inside a div element, like so:

td.container > div {
    width: 100%;
    height: 100%;
    overflow:hidden;
}
td.container {
    height: 20px;
}

<table>
    <tr>
        <td class="container">
            <div>This is a long line of text designed not to wrap 
                 when the container becomes too small.</div>
        </td>
    </tr>
</table>

This way, the div's height is that of the containing cell and the text cannot grow the div, keeping the cell/row the same height no matter what the window size is.