We almost certainly avoided worse outcomes but I don't think its entirely accurate to say we avoided bad infection/fatality rates relative to our neighbours.
If you exclude nations with less than 1M population the deaths per million list looks like this:
1. Belgium 808
2. Spain 660
3. UK 552
4. Italy 547
5. France 438
6. Sweden 418
7. Netherlands 343
8. Ireland 331
9. USA 307
10. Switzerland 222
While we have significantly better results than some of the worst impacted countries I don't think we have especially great results either. There are plenty of neighbouring countries that have massively outperformed us, Portugal (133), Germany (102), Denmark (98), Austria (72), Finland (56) for example. We reacted faster than many countries and yet later than we should have, allowing Rugby fans to travel from Italy for a game that was cancelled, and allowing thousands to return from the Cheltenham Horse Racing festival and from ski trips in Northern Italy without any quarantine being imposed among other issues.
I have some hope that we are past the worst of it and we may finish down this list as other countries see their final fatality rate continue to increase. I also think there is a possibility that we are tracking deaths more diligently than some other countries, though that is not based on much more than a few headlines and some hope, we also are testing at a very high rate relative to other countries. I have paid far less attention to the details in order to maintain my mental health as I found myself getting overwhelmed in early April.