Some good tips in here, but I was also facing issues once I'd wrapped the block of text in a <p> tag and some text within a <font></font> tag and added a CSS style to adjust the line height to try and make the gap even smaller.
I.e. <p><font style='font-size:20px; line-height:90%'>Some multiline text goes here</font></p>
I found that the additional line-height in this in style wasn't being taken into account by the Power Apps html control parser. To get this to work I found I could remove the paragraph padding around the top and bottom of the block of text and control the line height precisely by removing the <p> in favour of a <div> and adding the line-height style to that.
i.e. <div style='line-height:90%'><font face='Calibri' style="font-size:20px;line-height:50%'>
Thought this may be useful for others having the similar issues.