Hi Webby. If there is no pulling sensation through the steering wheel when this happens, then more than likely the issue is coming from the rear if the car.
So if follows that if you do feel a pull through the steering in time with the car wondering off line, then the problem will be at the front most likely.
Bushes, tyre condition and set up are the main factors.
Given we had time, I should have given the car a good look over really, but I did notice your rear bushes are not new, and tyres are old and worn with some damage on the left rear.
So one of, or a combination of those "could" give you the symptoms described. Most likely in fact but without seeing it I can't say for sure.
Tyre wear on a good set up car will give worn shoulder on the front. So a rounded profile, which ime means the front wants to roll off raised imperfections in the road.
The rear does the exact opposite, and wears the middle. So gives a squarer profile, this, ime, gives a tyre that wants to clime out of a team line for instance.
So, as I understand it, and I'm still learning Obviously, as the front and rear roll over the same bump or tram line, the front will react differently to the rear. Front will want to sit in a tramline, and the rear will want to clime out of it.
That's a massively symplistic view, and there's numerous combinations of worn parts and set variations that give loads of odd characteristics. But hopefully the above will give an idea of what to expect as a cars handling degrades.
Solution ime is.
Rectify steering and suspension faults.
Set up.
Fit new tyres.(not Falkens, not a stable tyre)