There are two separate questions here.
Can a British citizen marrying you in Saudi Arabia sponsor you as a spouse in the UK?
Can you in turn sponsor your first wife to the UK?
My understanding is that neither situation is possible.
For a foreign polygamous marriage to be recognised in English law, neither party must be domiciled in England and Wales. As the British citizen would most likely be domiciled in England or Wales, her participation in a polygamous marriage would not be recognised in UK immigration law. Therefore, she can not sponsor you to come and live with her in the UK.
Assuming that she is not domiciled in England and Wales, the marriage will be recognised, but only one spouse (typically the first wife to enter the UK, not the first one to marry) of such marriage is allowed into the UK. As your British wife will be the first spouse to enter the UK, your other wife will not be allowed to come to the UK.
Casa is our resident expert on matters touching on such matter. I would wait to hear from
Casa before progressing this query further.
Further reading
Marriage; specifically see Sections 2 & 8
Polygamy
IMMIGRATION DIRECTORATES' INSTRUCTIONS: POLYGAMOUS AND POTENTIALLY POLYGAMOUS MARRIAGES
Domicile
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.