Hi Lynne,
Matsu-no-ke (spirit of the pine tree) was a design conceived by Stevens & Williams. It was patented by them in 1884. The flowers are typically small & overlapping, & joined to rustic branches. They have a look of cherry blossom about them & were inspired by Japanese art which became very fashionable in England & Europe in the later 19th century. The originally Matsu-no-ke pieces were very elaborate, usually very fancy baskets, rose-bowls, vases. The flowers were usually clear, not coloured, & applied to coloured cased glass items. I sadly do not have any true Matsu-no-ke items in my collection, but I have a lot of pieces with applied flowers! There are so many types of applied decorations featuring flowers & also fruit, on Victorian art glass.
There are some Matsu-no-ke examples illustrated in Gulliver, & these are all noted as being marked with a registration number.
Many other companies made vases & the like with applied flowers, in England & Europe. Without a marking or documented pattern, it is hard to identify these items.
Anyway, it's a lovely piece, great colour, too! I like it!

A denture cleaning tablet is good for shifting the crud at the bottom of old vases, by the way. Just put some water in the vase & pop the tablet in. Leave it overnight if possible & you will find that the dirt is loosened up considerably.