Still serious enough to be arrested, and as soon as he's arrested the US authorities will request extradition which the UK will agree to. Leaving the embassy is certainly going to lead to a life behind bars in America. It doesn't matter what any of the charges are outside of the US.

If that was going to happen then why didn't it happen when he was in court in the UK?

Remember, he was in the UK on bail for months before he went near the embassy.

A year and a half on bail, from 16 December 2010 to 19 June 2012 per https://en.wikipedia.org/wiki/Assange_v_Swedish_Prosecution_.... Also per that Wikipedia article, he fled to the U.K. while under suspicion in Sweden, and "He left Sweden on 27 September 2010. The Swedish authorities have asserted that this is the same day that they notified Assange's lawyer of his imminent arrest."