We're definitely getting better at it and having Bruno as a 4th attacker helps us to press higher up the pitch.
Something I noticed about Southampton on Monday, was they were closing off all the options to the player on the ball, and pressing players without the ball. We really struggled to find a way out. Whereas, we seem to press the player with the ball but leave them options to pass before we press the receiving player. Not sure if this was due to tiredness or not, but as other posters have suggested, I think there is room for improvement but we're a lot better at it now than 18 months ago. For example, Martial put in a really good shift pressing on Monday, which is something he is learning (maybe from Ighalo?), as well as Ole. He's adapting his game for the benefit of the team performance, whilst also enhancing his overall contribution.
City and Liverpool also press as a group/team, which helps them win the ball back quicker.