They can and they did. When they released the new iPhones in September they increased the prices all over Europe at around the same percentage as they did now with the iPads. And the new MacBooks next month will also be much more expensive than before. And maybe they will correct the price of things like the Studio Display, too, despite it getting zero updates. And other (tech) companies will undoubtedly do the same if they didn't already.If this was inflation and devaluation of currency, then explain to me why today, when Apple increased the price of the iPads, they have NOT increased the price of the iPhone product line, or the Mac product line? or even the Apple Watch?
And about doing the math:
£569 is $643,28, without VAT that would be $545,15 and without other fees probably more like $535.
£669 is $756,34, without VAT that would be $640,97 and without other fees probably more like $630.
Apple sells the iPad in the US for $599 without tax.
If you compare the old (VAT and fee adjusted) price of the iPad Air in the UK in $ you clearly see that no matter how you calculate Apple did earn much less with the iPad Air than they did in the US. So they adjusted the price. Now they earn a little bit more with the iPad Air in the UK than they do in the US. They did not price it a the correct current exchange rate because they probably expect the pound to loose more value in the future (as they apparently do with the Euro) and also they don't wan't to adjust their prices all the time.
But if you do the math, as you suggested you can clearly see that the problem is the value of our currencies and that the proportions are changing.
PS: For this price change it is completely irrelevant that the iPad Air din't change a bit.