Moss on flowerbeds isn't uncommon, especially if the soil is heavy and the area's shady and damp. However, it is also a sign of uncultivated soil, and may indicate a depletion of nitrogen, so its probably best to turn the soil over and incorporate something like Growmore; adding a bag or two of composted animal manure would be useful too - best done from mid March onwards.

Thank you. This is a problem that has perplexed me for a long time and yes the soil is heavy clay.
Thanks again.

if you can manage it, adding composted animal manures or your own garden compost will,over time and if added frequently, improve the heaviness of the soil.

Apparently the other plants are doing just fine and looks nice with the plants growing up through it. I wouldn't worry about it too much- except the weedy plants I'd pull up.

Our soil is a light peaty silt and has had plenty of animal manure and compost and Growmore over the years and even on the sunny parts is covered in moss. The plants grow well, it just looks unsightly.

Moss does provide benefits for the other plants - erosion control, moisture retention, flood mitigation, soil conditioner & weed control.

For further information and confirmation, you might like to read this
https://www.rhs.org.uk/advice/profile?PID=412

Whether you like the moss or not is entirely up to you. My point was that it can serve as a "place holder" until you decide what to grow in its place - holding on to important nutrients. For more information on the benefits: you might like to read this:

http://davesgarden.com/guides/articles/view/2249/#b

Here are the pros and cons of moss and how to get rid of it if you so choose.

https://pubs.ext.vt.edu/430/430-536/430-536.html