The reason why Alfred, did not take the throne was because, the British had said that they would keep their hands of Greece.
George (Then Prince William Christian of Schleswig-Holstein, was first seen as a potentional 'King of Denamrk' at arounf the time of his sisters wedding (Alexandra to the Princess of Wales) On of the Reason's for this was becasue there was 'no strings attached' in a sense.
Here is some information I found on the matter
"The vacant Greek crown was then offered to Queen Victoria's second son Alfred, Duke of Edimburgh, but the British government refused since there was an international agreement that established that no member of the British Royal family was elegible for the Greek throne. Neveertheless, England was deeply interested in Greece since she wanted to inccrease her infuence in the Aegean. If Prince Alfred could not be king, there were other candidates. and the elected was the second son of Prince Christian of Schleswig Holstein Sonderburg Glucksburg, the seventeen-year-old Prince William of Denmark. The Greeks accepted the choice. A King suportted by England meant the return of the Ionian Islands, now in British hands. Besides, Prince William was closely related to the British Royal family since his siser Alexandra had just married the Prince of Wales.
On March 30, 1863, the Greek National Assembly proclaimed William as King George I of the Hellenes. William,a frank and cheerful young man, who loved joking, was happy about acceptng the Greek crown, but not his father, Prince Christian, nor his mother, Princess Luise, who apealed toher daughter the Princess of Wales to influence the British government against the match and wrote Queen Victoria, looking for her support; but everything was unuseful against William becoming King of the Hellenes. Even King Frederik VII of Denmark supported the idea. Christian had to accept but he established some conditions: the three Great Powers must guaranteee his son 25,000 pounds a year in case of being dethroned and the Ionian Islands should be returned to Greece by England.On June 6, 1863, Prince William formally accepted the Greek crown.
In October that same year, the young King George arrived in Greece. He soon realised he had received one of the poorest, bad organized and unstable countries in Europe. The Royal Palace, where he would live, was in a deplorable condition, having been victim of vandalism since King Otto's departure. The Danish Prince faced the difficulties of his new possition with great aplomb, and he identified himself with his new country as much as posssible. He quicly lernt the Greek language and he visited every part of the country, even by mule or on foot. He remained Protestant but he paid a great respect to the Greek orthodox Church. King George forced his Greek ministers to frame a new constitution which resulted very liberal for those days. Altough he could appoint and dismiss ministers as well as to disolve the assembly, he involved himself as little as possible in internal politics. Most of the times, he left the politicians to resolv problems, interfiring only in time of crisis. He didn't favpour any party.
After four years of reigning, King George began to think in marriage in order to establish a dynasty. He tought Russia would provide him of a suitable wife since his future children would have to be Orthodox and only in Russia he could find an Orthodox princess. And so he did. In October, 1867 King George of the Hellenes married in the Winter Palace to the fifteen-year-old daughter of Grand Duke Constantine (Alexander II's younger brother), Grand Duchess Olga. Nine months later, the new Queen of Greece geve birth to her first son. He was named Consantine and soon was followed by six more children (4 boys and 2 girls), who grew up lovingly and naturally. ing George bought for his family a 40,000 acre property, fifteen miles north of Athens, which was named Tatoi. George gave tatoi a danish character; more trees were planted, the roads were fixed, Danish agricultural methods were introduced, barns and stables were built and Danish and Swiss cows were imported, and soon Tatoi had become a complete Danish farm.
Altough King George was a Dane in private, he was a Greek in public life. he had a compromise with the "Great Hellenic Dream", the return to Greece of Crete, Thessaly, Espirus, and most of all, Constantinople, then in Turkish hands."
