Thanks for all your input.
Astute of those who mentioned the sailing connection which indeed promted my original question.
As is now clear the higher your speed relative to the "drift" the less impact on the final outcome. For sailors the difference can be significant.
For ease of calculation, imagine crossing Solent to Cherbourg (180 deg) in a boat doing 5 knots. Assume that the tide is doing 4 knots, initially on 90 deg, then 6 hours later it changes to 270 deg. (Yes, I know that tides in the Channel don't reach 4 knots, and that they don't have a step change in direction, but the effects of the real tide will be the same.)
If you plot a tidal triangle such that your COG is 180, then you will make the classic 3-4-5 triangle: a 5 knot hypotenuse (boat speed), a 4 knot vector for tidal set, resulting in a 3 knot vector for boat speed over the ground. You will be travelling along a straight line between the Needles and Cherbourg, but your bow will be pointing at about 233 degrees, well off that line. After 6 hours, you will have got 18 miles closer to France.
If instead you point your boat's head at 180, then of course you will be swept up-channel. After 6 hours you will have been swept 24 miles off your direct course, but you will be 30 miles further south.
Now the tide turns. If you have been staying on the direct line, then you will now need to counter the tide in the opposite direction. You'll have to change your heading from about 233 deg to about 127 deg. You'll stay on the line, but you'll still only close France at 3 knots. After another 6 hours, you will have made 36 miles of the 60 mile distance.
What about the boat that was swept up-Channel? She keeps her head on 180 deg, continues to close France at 5 knots, but is now being swept down-Channel. After another 6 hours she has been swept back onto the direct line, but has now made her full 60 miles cross-Channel. She should be just entering Cherbourg Harbour, with the restaurants open and waiting.
Of course the same could be true more or less of slower aircraft - a microlight or a 152 enjoing a cross country with a 30 knot crosswind would notice a significant difference albeit in the aviation world wind reversal along a track are very rare.
Never the less it is interesting I think that what we intuitively believe is happening (in terms of the preferred strategy of following the magenta line) is in fact the wrong strategy even though the difference is small compared with sailinga yacht.
Thank you all again for an interesting debate - I have got another one for you along a similiar theme shortly.
