eBay is going to be your best bet. Typically Dyson doesn’t sell those smaller parts. However it might still be worth contacting support just to make sure.
Thanks IsiahH.
I managed to find out that the name of that part is a Swivel Lock Arm. I found the best deal from A S Electricals, they replied straight away, and it arrived as promised.
They warned me that there are 2 different arms for the DC40, mine has visible ribs on top, and they are not interchangeable.
Installation was fiddly, especially to make sure that the wires to the Head are not trapped. Also, watch the white cogs, as they could get separated and will need re-aligning, so have a good look, and take photos before taking apart. I am still unsure whether they are properly meshed, as it take an extra tap on the wheel carriage to lock it upright.
Despite the fiddliness, it’s great to see so many Dysons being repaired, thanks to the existence of the community.
Roy