First, a few clarifications on the Barons.
Samuel Selig (later de Kusel) was born in 1849 to Louis and Mary/Rebecca. He married an Italian woman, Elvira Chini in 1876.
Arthur Adolphus de Kusel was the son of Adolf de Kusel (b. 1836 Mecklenburg-Schwerin), who had been granted the title Baron in 1892.
According to FindMyPast, there was also an umarried Lea Kusel, b. 1839 Germany, living in Liverpool in 1861. Louis' and David's sister?
Now, to your questions Carole.
If Mary had not been Jewish, conversion would have been a possibility. But, the difficulty may have been that Louis could not prove that his parents were Jewish. Therefore, although they may well have found a Rabbi to marry them, unless it was Rabbi authorised under British law to conduct a wedding, the union would have been illegal. Such clandestine weddings did occur; they are referred to as stille chuppah.
As for a Christian ceremony, I'm not sure. It was my understanding that couples wishing to wed had to produce baptismal certificates before they could be wed in a church. I have always wondered how my Jewish great-grandfather married in a church!
The registry office would have been the easiest option.
Immigrants/aliens were at liberty to marry whenever they wished to. However, a British woman marrying an immigrant would have actually lost her status as a British national, and have been regarded, under British law, as a foreigner.
Justin