Slow draining bathroom sink

[KenB]

Our bathroom sink drains painfully slowly and I cannot work out why. I have plunged it many times and poured all manner of caustic chemicals down it so I don't think it is blocked. I have also removed the U bend, which was clear, and looked down the down pipe that runs under the floor, and that as far as I could see (not far) was also clear.

When the sink drains you can hear a slow trickle, which sounds like free running (if slow) water.

The shower, sink and bath all seem to join into one drain as there is only a single pipe going through the wall outside (into the stack).

What could be the problem?

Here are my uneducated and unfounded guesses:

1) The top of the U bend is too high compared to the bottom of the basin. Could this make any difference???

2) There is some blockage where the pipe that runs vertically from the sink under the floor bends towards the drain.

3) The sink is too far away from the drain so the slope of the waste pipe is incorrect under the floor. It is in fact only 7 feet, three feet less than the max stated in this article.

Any advice appreciated!