Big lockdowns last year definitely made an impact in England and Italy. I expect it will be the same now. What failed here in UK was the regional approach, the continuous attempts at unfounded optimism, and the attitude that covid-related rules were just another game to play and cheat at (like a minster saying that a scotch egg is “a substantial meal” which can justify going to the pub...).
The population doesn’t take the message seriously unless the gravity of the situation is stressed and the necessary plans are clear, simple, consistent throughout, and ruthlessly enforced. When most of that happened, lockdowns worked.