Are Her Majesty's grandchildren...including Prince Harry allowed to marry a Saxe-Coburg and Gotha?

Changing the name didn't prohibit anyone from marrying a distant cousin from one of the many branches of the Saxe Coburg clan. There's no law or rule against it.

There are actually next to no rules or laws concerning who can marry into the royal family. Even the rule against Roman Catholics has recently been abolished.

Edit: LLwynog, you seem to be oddly unaware that the Hanovers were direct descendants of a long line of English and Scottish monarchs. George I was the great-grandson of King James VI/I Stuart and therefore also a direct descendant of Henry VII Tudor and all of the Stuarts and Plantagenets and William the Conqueror, plus the earlier Anglo-Saxon kings. If he hadn't been, he would not have been offered the throne.

They didn't teach you this in school? Funny. I'm in the US, and they taught it to ME.

Members of the British Royal family are allowed to marry anyone they wish as long as they the permission of the Monarch.

I can't imagine a British consort with the surname 'Saxe-Coburg and Gotha' - it still sounds too German for the UK.

Yes, because they are free to marry whomever they want

The House of Stuart should just be revived. The Germans should have never got the throne.

Lili is right but I personally think her Majesty might oppose out of respect.

This is a free Society and weather you be king or a tramp you have the right to do what you wish.

No, though it might be betraying their line of heirs...who would likely wind up being deformed from having parents too closely related.

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No, they would not ! Interbreeding doesn't work !