The validity of the charges in Sweden aren't his only problem. They could drop the case, he'd still be in trouble with the UK because he fled bail. Bail is an agreement between you and the court. You agree to appear as ordered, and they let you out of jail. Often there is also a monetary component to try and ensure your compliance. However regardless of the details, you are legally required to present yourself in court when ordered.
So when Sweden said they wanted him, the UK arrested him. In the EU there's some pretty strong extradition rules so even though the UK had no issue with him, their extradition treaty with Sweden required them to arrest him. He was granted bail, and the monetary component was paid for by supporters. At the point, he had to wait for a court date when the UK courts would determine if the extradition request was valid. At that point if they did, they'd hand him off to Sweden, give back his bail money, and would be all done as far as they were concerned.
They did find it was a valid request, he challenged that finding, and so on up to the UK's high court. They ruled that yes, it was a valid request. Remember this has nothing to do with guilt, they are not interested in that. Their only interest is if the extradition request is a valid one per the treaty. It was, so they said "Ok, you have to turn yourself in and we'll ship you off to Sweden." He decided not to, and instead fled.
Well at that point he become a criminal in the UK. They now had a criminal interest in him since he'd broken UK law by skipping bail. Doesn't matter anything about the original charges. This is a separate crime, and it is an ongoing one, so no statute of limitations.
That's how it works basically everywhere. If the court says you have to how up, and you don't, that by itself is a crime.