March is a good time to plant seeds, I,d go to a garden centre or somewhere selling seeds and look for annuals. The packet will tell you what they are, how tall they will grow and if you look carefully they will say if they make good cut flowers, some will also say easy to grow.
Follow the instructions on the packets and I hope the weather is kind to you

Great time of year to tart thinking about some lovely perennials too. Most of the daisy type perennials are good as cut flowers, and you could do some Dahlias too...start them off under cover soon. I love alchemilla Mollis in vases, and chives work beautifully as well...dead easy to grow too... And wonderful in a new potato salad of course! Yum! I believe Cerinthes are good in vases, and you could sow these now. Cosmos are fab, and they can be sown under cover now as well. Zinnias and of course Helianthus...annuals and the perennial types. Inula is a wonderful shaggy yellow daisy as well....enjoy!

One of my favourite cut flowers are Rudbeckias. They don't flower very early, but go on into the autumn. There are different shades of yellow and rust. You can also get double flowered varieties, and they last a long time after cutting :o)

Sweet peas are lovely too. If you haven't got room for the tall ones look for the Knee High or Jet Set varieties.