I think it should be noted that regarding jewels this period focused on elements which we today usually perceive as embellishments of the garments rather than pieces of jewellery. The jewels framing the head-dress or the cleavage were usually stitched onto the fabric. The necklace formed only a small part of this rather different type of "parure". Holbein's portrait of Jane Seymour illustrates that quite well. Here's a sharper version:
The combination of pearls and gold set gemstones was fashionable during most of 16th century. On closer inspection one can see that the elements between the pearls depict stylized Tudor roses. The necklace worn by Queen Mary I on numerous variations of the portrait posted by Dawn is similar, but not the same. The roses alternate with three pearls in each row instead of two:
And the roses seem to be more elaborate than the ones in Jane Seymour's "parure" as can be seen in this variation of the painting. Note that the rose above the "T"-shaped pendant completes it to a cross and the lowest part of the "T" mirrors the rose which emphasizes the impression:
Of course Mary might have used pearls and jewels which previously belonged to Jane Seymour, reset or not. But these strings of pearls and Tudor roses existed in abundance and were not only worn by queens but also princesses.
Catherine of Aragon is wearing them around her cleavage:
Catherine Parr with a similar necklace:
And finally Mary's sister Elizabeth as princess wearing three strings of pearls interspersed with roses around her cleavage and on her head-dress: