The power bank in question is a Anker Astro E7 rated at 26'800mah. It's input is 5V/2A and it's output is 5V/4A (Total). I believe it has 2 2 amp usb outlets hence the total (I could be wrong on that).
In relation to the Solar Panel, I'm still thinking specifically which panel to get, I don't exactly intend to get something cheap off eBay like those cheap £1.99 panels but since I'll be charging a power bank I won't be going for something to heavy. I was thinking of the Anker Solar PowerPort. It's advertised output is 5V/ 3A. I believe the panel is rated at 21W.
Hmmm. Anker have a good reputation, but they are rather vague when it comes to advertising precise specifications.
For example they say the Solar PowerPort is rated at 21W, but its maximum output is 5V/3A which is 15W. I'm not sure what the 21W figure means. If I had to guess, I'd suggest that the panel could deliver 21W in ideal conditions - i.e. bright sunshine, with the panel orientated exactly perpendicular to the sun's rays. That would imply that it would be capable of delivering its maximum output of 15W even when the conditions weren't quite ideal. (And presumably when conditions are ideal, some internal circuitry limits the output to 15W and the rest is dissipated as heat, or something like that.)
When we're looking at capacity, I think Anker assume everything runs at 5V. So the capacity of the Astro E7 power bank is 26,800mAh x 5V = 134,000mWh = 134Wh. As you say its input is 5V/2A which is 10W, so it will take at least 13.4 hours to fully charge - more if the charger isn't delivering the full 2A.
If we want to gauge how the power bank would work in connection with the solar panels, I think my experience of the panels on my roof is relevant. (See graphics in previous post). My panels are rated at 4kW, but on that sunny day at the end of May the most they delivered was about 80% of that, and averaged over the entire sunny day the output was about 40-50% of that. So with the Anker panels, with a capacity of 21W, you might reasonably expect to get about 8-10W averaged over the whole day, if you put them on my roof (azimuth angle 20° from south, slope 22°). If you laid them out on a horizontal surface you'd get a bit less; if you hung them on the back of a rusksack as in the Anker illustration you'd get a lot less; if you were using them oop North instead of in Maidenhead where I am you'd get less; and of course if it's not sunny or not summer you'd get a lot less.
So if you laid out the panels on a suitably inclined south-facing surface, in the south of England in the summer, this implies it would take a full sunny day to fully charge the power bank. That's the best case for the UK. If you wanted these to charge your power bank whilst hiking in Death Valley, say, things would be a bit different.