I can only really speak for the UK. The UK hadn't persecuted Jews for many centuries before the holocaust and had allowed Jewish immigrants into the country to escape persecution. There was a strong tradition of Jews living happily in the East End of London.
The rise of right wing sentiment did change that to some extent but only for a minority. There were definitely issues but the country as whole and government certainly weren't anti-Semitic.
When Hitler started changing laws to persecute Jews, the UK kept an open border and allowed them to settle in the UK. They had to have a certain amount of money though. There was a point where the UK was the only place a Jew wanting to escape could go. Most of continental Europe was under German control, threatened by it or wouldn't allow Jews in. America shut its borders too.
So naturally, seeing Jews as victims even before people knew about concentration camps meant finding out about the camps was devastating to the UK population generally. The UK propaganda machine also exploited it to say how right the UK were to have fought Hitler.
When the UK army liberated Belsen, images were shown across the UK. My Nan told me people fainted and cried looking at the images in a cinema. I don't think anyone could have been imagined the holocaust before it happened.