When riding past parked vehicles you should be in the right part of the lane, unless you have to give up position for a wide oncoming vehicle.
Staying in the right-hand part of the lane still doesn't guarantee that a vehicle has seen you. Look for the tell-tale signs of a driver about to do a u-turn: the driver craning their neck to see behind, the wheels on full lock, and the driver not pulling out of the space even though there was room on your side of the road because there was a vehicle on the other side that would have prevented the u-turn.
If you are travelling towards a car that's on the other side of the road and the driver is thinking about doing a u-turn, keep an eye on your escape routes if the driver pulls across in front of you.
If you are driving past a large vehicle, that vehicle could be obscuring the vehicle in front of it, or pedestrians.
Slow down if you need to, and remember that you can use your horn.
As well as scanning up the line of parked cars you will also need to pay attention to what's coming towards you because you will be closer to that lane.