This document from the National Oceanography Centre (formerly the Proudman Laboratory) (http://www.kayakwaveology.com/files/ProudmanTidalPaper.pdf) describes the method the Admiralty uses to measure the currents. To quote the relevant section,
To obtain tidal diamond data, a small boat is anchored over at least a 12 hour period at the site of the tidal diamond. Every hour, a current meter is deployed over the side of the anchored boat and the current is read off with the meter just below the surface. The measurements are made during a meteorologically quiet period (otherwise residual flows have to be removed), and factored based on the mean spring and neap tidal range at a chosen reference port to reflect these conditions. The current variations are given at hourly intervals over a 12 or 24 hour period related to the time of high water at a given reference port. The data are not analysed but the results derived from using the tidal diamond data are, at best, equivalent to using the harmonic constituents M2 and S2 (the gravitational effects of the moon and the sun respectively).
What this means is that the Admiralty uses an extremely small, very limited set of data to determine what the currents are doing. They don't analyze the currents for the harmonic constituents as there isn't enough data (harmonic constituents are the standard method by which tides and currents are reduced to a set of numbers that can be used to model and predict them, typically it takes 3 - 5 years of hourly data to generate enough harmonics to be useful) but instead relate the limited data set to the times of high tides at a nearby reference port.
To give you a counter-example, to predict the tides to the centimeter level and within +/- 2 minutes or so, between 22 to 50 harmonic constituents are normally required, and sometimes many more. The method the Admiralty uses only implies 2, as the paper states. This means that the curve for the currents is disjoint; it consists only of line segments between H-6 to H+6 in steps of an hour (what we are calling the dots). This is what we see when looking at the Navionics app, for example.
Notice how odd the curve is. It's only line segments connecting the dots. There isn’t really a time for slack current as it jumps from ebbing to flooding (and vice versa), and a long time of maximum flood current but hardly any at all at max ebb. This tells us that they are not using harmonics, as the curve would be smooth and continuous. Unfortunately, mathematics says there are an infinite number of curves that can be fitted to the dots, all of which are valid but only one of which actually describes the currents.
The paper goes on to describe the use of a hydrodynamic model of the oceans around the UK to estimate the harmonic constituents of the currents, and this model can indeed give predictions of the currents. However, it's a model, and obviously we don't have it nor the horsepower on the iPhone to run it. It's also been tweaked to produce results that are consistent with observations (the ones used by the Admiralty initially to create the current predictions) and it's not clear to us that this is appropriate. It would have been instructional to know what the model produced with and without applying the observations - the currents may have come out much differently, which would imply the model was flawed.
In any event, this explains why we cannot find current observations to analyze. There isn’t enough data TO analyze, and without data there can be no harmonics, and no harmonics means no predictions. We were also right in assuming that a hydrographic model was used to predict the currents, models that aren't open to the general public. These two conclusions imply that accurate predictions outside of a large agency with manpower and money to burn are, if not impossible, then very very improbable. We ourselves would not use these current predictions with any confidence; they are based upon too limited data and/or a lot of assumptions, none of which are explained.
So, that's where we stand today. We hope this helps explain why some programs have current predictions while we do not. We hold ourselves to a higher standard, as we refuse to use limited data to draw broad conclusions. If you have good luck using these predictions, then we applaud you, but our opinion is to be aware of their limitations and don’t trust them completely.