I think that it is difficult to define antisemitism by a single comment or view (unless someone just admits that they dislike Jews, which is unlikely, at least among the well educated). However a series of views and statements can paint a picture, as can a desire not to engage with any counter arguments:
Anti 'Zionism': As in 'I am not anti Semitic but I am anti Zionist'.
I think that if you are against the existence of the state of Israel in any form, that is antisemitic. If you are against current Israeli policies or of the way they treat minorities, that can be clearly stated and is not antisemitic. In Israel, there is a huge plurality of views on these issues.
Anti circumcision:
Again, perfectly reasonable to be anti circumcision and to believe that it is wrong. However, to grossly overstate how wrong and overly focus on one community who perform it is antisemitic, in my opinion.
Never speak out against growing antisemitism in this country or listen to the views of Jewish people who experience antisemitism, to never acknowledge the cultural and philanthropic contributions of the Jewish community.
This clearly shows where someone's sympathies lie.
If you put the above three together, I think that you can judge a person to be antisemitic.
I think that the UK is far better than the continent. My mother lived in France for 10 years as a secular Jew (without telling people she was Jewish unless asked) and witnessed a lot of overt antisemitism in people's comments ('I really liked him but did you know he was a Jew' was one of many). There is no question, however, that antisemitism is growing here and the Jewish community is concerned about its security.