replacing the drop-links (also called stabiliser-bar links or anti-roll bar links) has sorted my car also, except for a slight knock from the OSR.
I'm afraid you will need an angle-grinder to get the old ones off though.
If you have ordered the genuine Toyota drop-links, you will need to buy some nuts from Toyota too. They are 14mm Metric-Fine (finer thread than regular Metric), and you will not find them at any hardware stores. The existing ones will be ground off with your angle-grinder of course.
After three hours of driving around Engineers suppliers and hardware-stores on saturday morning, I made a last-ditch attempt to see if my local Toyota dealership workshop was open, and to my joy, their parts dept. was open and supplied me with the necessary nuts.
They need to be locking nuts (Nyloc or similar). The ones I got were perfect and had a crushed end which made them lock. Apparently they are used on exhausts. I'm afraid I don't have the part number.
The rears are easy compared to the front - you have good access to get the angle-grinder on the nuts. I recommend you do the lower nuts on each side first, then the anti-roll bar will be loose so you can rotate it where you want, making it easier to work on the upper nuts.
You'll see what I mean.. the drop-link is basically a horizontal link between the anti-roll bar and the wishbone, so it's bolted to the anti-roll bar at the top, and the wishbone at the bottom, on each side of the car. Do the bottoms first then the anti-roll bar isn't connected to the wishbones any more and can be rotated around for doing the tops.