Hello,
attached is a simple writer document. The wrapping in the table cell in the text area works well. The copied cell in the footer table doesn’t behave as well. Why?
no-wrapping-around-image-in-footer.odt
Very strange: if I copy your image in a blank document, wrap options work only in main text area. I can’t even get a correct header (both header and footer exhibit the same nonsense behaviour). To be sure, I tested outside table.
Here LO 6.0.7.3.0
It seems that wrapping does not sufficiently work in tables located in header or footer. LibreOffice 6.2.0.3 and Apache OpenOffice 4.1.6. and Oracle OpenOffice 3.2.1. and OpenOffice Portable 2.4.1. Must be a very old bug. In OpenOffice 1.1.5 the wrapping works okay.
I only checked the tables because of @Addi’s question. And, yes, you are right, the wrapping is confused even in regular text environment in header/footer.
The “explanation” - in general - could be, that entire wrapping in headers/footers is trashy. I have never heard of this bug for years until today. - If I needed a graphics object in header/footer I would basically anchor as character. For many cases it is the stablest way to do that.
And: For text area backgrounds I never have had bad experiences to anchor graphics objects (to paragraph) in header/footer. It simply worked well.
@Grantler: anchoring graphics to the desired position needs a lot of practice. Apart from To Page which has non well described constraints, the other modes work quite well if you understand thoroughly (this is the important word) what’s going on. I recently experimented with To Character to get interesting effects.
It appears this is a bug and no fix is presently available. Therefore I suggest the following workaround.
Your header and footer have a specific structure. You can therefore create your container table with four columns instead of three. The extra cell (column) will only contain your picture. Being the only object in the cell, text wrapping does not occur.
Of course, go to Table>Table properties, Columns tab to set column widths to the desired values (unequal columns).
I meanwhile managed it with spaces and manual wrapping. 
But nevertheless thanks for your suggestion. In some cases it would be a workaround but in my case unfortunately not. In the lines above and below the picture are addidional address data (I removed in the example). They have to be left alligned with the left side of the image. But the suggestion brought me to the idea of combining cells. And that seems to work in footer table well. An example of that (also more or less dirty) solution I attached in my following answer.
Creating more lines to vertically align data in the “critical” area is a common trick. Outside the “critical area” cells are combined to result in a single one as you noted. Usually text is vertically centered in these tall cells.
ajlittoz brought me to the idea of combined cells (see my comment in his answer). I created an example with that possible (but also more or less dirty) solution: more-or-less-dirty-workaround.odt
It is not a “dirty” solution. It is a common sense solution which is routinely used in web sites.