He is really bad at time management and even when he's late, shows no sign of being in a hurry.
He is a bad timekeeper and shows no sign of being in a hurry even when he's late.
「時間にルーズ」＝ bad at time management, bad at timekeeping, not good at time management・timekeeping/always turns up late
「急ぐ素振りもしない」＝ shows no sign of being in a hurry
「彼は時間にルーズで遅れてるのに急ぐ素振りもしない」＝ He is really bad at time management and even when he's late, shows no sign of being in a hurry. / He is a bad timekeeper and shows no sign of being in a hurry even when he's late.
イギリス 
