When we formulate/ask a question, we place the auxiliary verb before the subject of the sentence. However, Present Tense and Past Tense verbs do not have an auxiliary verb, so we use a 'dummy' auxiliary, from the verb 'to do'.
In your question:
How does England solve their striking problem?'
'does' is the auxiliary verb.
How can we ask England how it solved a problem, when the problem isn't solved? 'their striking problem' implies the problem is continuing.
So, the first question needs to be rephrased:
"How does England solve a strike problem?"
or
"How did England solve its strike problem?"