I'm the only palm tree native to Europe, my ancestors were found across southern Europe and the Mediterranean. I'm quite slow-growing, and am happy in borders or pots. The climate here in the UK is changing and the weather is often very similar to the Mediterranean, so that should suit me! I'm not keen on the idea of my roots sitting in cold wet clay soil, but generally I will cope with everything the weather throws at me.
Chamaerops humilis
Well, my rate of growth is determined by three things: location, location, and location! Out in the wild in a mild sunny climate with plenty of annual rainfall I will grow in a large tree - I've got cousins in Cornwall (and central London) who are really big and dramatic. If we consider a typical British garden with cold wet winters and variable summers I might grow about 5cm each year. If we have a mild winter and a long warm summer I might grow 10cm a year.