Garnets are beautiful, I have some earrings and a necklace from my grandmother, she brought them over from Czechoslovakia when her family emigrated to the US.
Five thousand pounds or around sixty five hundred US dollars would be about right. Unfortunately, the gold is lower grade plus the family doesn't have positive proof such as a document that the set belonged to the Swedish Royal Family. Garnets are also unfortunately consider semiprecious gems. The appraiser didn't mention the grade of the pearls or diamonds.