Dyson Tech may certainly be right.
Try bypassing the brush toggle (the middle switch in the above picture); if the brushes stay on, the switch is bad.
However if you still have the same problem, it may be the reset switch.
It's the far left button in the above picture and it looks like this:
Now, you could probably get a new switch, but do you really need that switch?
All it does is return the brushbar to the default state when you turn of the vacuum and return the handle to full, upright position.
I say just bypass it.
To do that, disconnect the two leads from that switch.
One goes down to the brush head.
The other goes to the middle switch; it's a short wire, about 8 cm long.
Disconnect the other end of that one from the middle switch.
At this point, you'll have one open post on the brushbar toggle, one wire that comes from the brush head, and one short wire that's not connected to anything.
It would be great if you could simply connect the wire that goes down to the brush head directly to the post on the brushbar toggle.
Unfortunately, you'll notice the connector on that wire is too small for the post on the middle switch.
So you'll need to either cut that connector off and put on a new one (you could use the connector from the short wire), or connect the wire from the head to the smaller end of the short wire.
This is what I did in case I ever decide to replace the reset switch.
Likewise, I let the reset switch in it's location so I know what to order if needed.
In the end, this is what I have:
If you leave the brushbar off when you power off the vacuum, it will still be off the next time you use it.
Other than that, everything will work the way it always has.