My sister and her husband separated amicably around 6 years ago after having been married around 3 years. They married in England but went to live in Greece shortly afterwards. About a yr ago, the husband returned to the UK and is getting married this week. My sister has no issue with this but has never signed any papers or received anything about a divorce. Whenever she asks, he ignores her and doesn't reply to messages. The solicitor who was handling the divorce now says he isn't so my sister has resorted to emailing the local court for answers with no success. Could he have divorced her without her knowledge? He has her address and knows how to contact her. What should my sister do next?

Yes, it's possible the divorce was granted and she was never notified. It should happen, but I've seen it happen in the US.

What is her concern in all of this? His remarrying? Her possibly legal responsibilities? Whether she's divorced?

She would know where he/she both lived. Contact the Court Clerk at both locations and ask about the filings. I'd call, not email, or I'd write a letter, signature upon delivery.

... The solicitor who was handling the divorce now says he isn't so...

What makes her think that the solicitor "was handling" a divorce? It could be that one or both spouses simply consulted the solicitor, but nothing more was done. If the solicitor filed divorce papers he should be able to say.

She also might be able to contact the agency in her country which is responsible for keeping track of "vital statistics", such as birth certificates, death certificates, etc. For all I know they also track divorces.