I'm new to Affinity Designer. Like many I'm sure, we are looking to escape the Adobe tyranny. However, our work flow is important and the more seamless a transition the better. However, like all of you here, exporting to SVG file format to import into a 3rd party CNC program (or other) is wrought with difficulties. Vector designs went seamlessly using Illustrator but not with AD - anything I did via AD ended up importing really, really small. I did not want to have to rescale in my CNC software as I took painstaking efforts to make sure I did that in AD (or AI). Alas, a big thank you to @angusware for his solution. Albeit I found a few minor mods that seemed to work just fine too. So below are my slightly amended instructions in hopes it saves someone else max. time trying different permutations to try and figure this out. Btw - it is July 17, 2019 and I'm brand new to the Affinity ecosystem, so this problem clearly continues to this day as I see many on this thread were posting over the last year or two. Hopefully the folks at Serif will rectify this in coming releases.
1. Select “New Document” from the pull down menu.
2. Set up the document units to pixels to use pixel measurements in place of millimetres,
3. When creating your vector object, and by way of example, if desired size is 100mm square, make the object 100 pixels square (ie. 1:1 ratio).
4. Save the document in AD’s native file format for future use or edits.
5. Export the document using the export option in the file menu.
6. Select 'SVG (for web)'. Click 'More' for extra options.
7. Deselect 'Set viewBox' and select 'Add line breaks' (I also tried unselecting 'Add line breaks' and it also worked, in other words, didn't seem to impact either way).
8. Export the file.
9. Import into your 3rd party CNC/laser cutting program
NOTE: I excluded the code/text editing instructions angusware referenced in his workaround, this apparently was not required at my end. And I'm thankful for this. Maybe the absence of having to do this was suited to the 3rd party CNC software I'm running? Who knows, however, if you get away with having to do it, great . . . . it's one less step!
Cheers!