Exactly! You can alway "adjust" something. You can only "readjust" something if it has previously been adjusted. Think of it as a short way of saying "adjusted again". As long as you do not say "readjust" for something that cannot possibly have been adjusted before you will be fine. Very very few people in the whole world could correctly say "I will need to readjust to life in space". Everbody could adjust to life in space.

Daisy, I've adjusted the paintings on the wall so that they're perfectly aligned with the floor, but it seems that they've become crooked after last night's exhibition party. We have another party in two days, but I am so busy with things that I don't have time to deal with this. Could you go and readjust the paintings so that they're perfectly aligned with the floor? If you adjust something once and then it becomes misaligned or wrong, you have to readjust it in order to bring it back to order, to bring it back to its normal state. I've adjusted the thermometer to 22 degrees, but somebody lowered it to 18. I'll have to readjust it. (in this case, readjust means to put it back to 22) I've adjusted the thermometer to 22 degrees, but somebody lowered it to 18. I'll have to readjust it back to 22. Actually, 22 was too much, I'll adjust it to 20 this time.

They are very similar. So much so that I doubt a native speaker would really even notice the difference in conversation let alone pick you up on it. Stick with adjust if you are unsure. To re-adjust would have connotations of either having to repeatedly adjust something (as in adjust it again) or to adjust something back to how it was originally. "I need to readjust this seat, its getting on my nerves" "We need to readjust the layout of this website, its still not working for me" "I need to readjust to life in England" would imply that you have already previously been used to life in England. "I need to adjust to life in England" could be said by anyone when they arrive.