Looks like the bulb Ornithogalum nutans?

yes i agree it does. one of its common names is 'star of bethlehem'.

As this is the first time I've used the site I hope I am doing the correct thing to thank the two people who have responded to my question. As I don't know what the plant is I cannot argue with those who responded, however for some years my wife has had what she refers to as 'Star of Bethlehem' and both the white and mauve variety grows in plastic hanging pots about nine inches in diameter. The flowers have five petals (I think) are about the size of a two pence piece and grow on a plant which has light green foliage and "roundish" leaves. As an indication of how the plant appears, chickweed comes to mind inasmuch as it does not have stalks like the one I am querying. Perhaps my wife has misnamed the plants she refers to as 'Star of Bethlehem', which may be calendula?

Welcome to GoY, Flowerpotme, and I can tell you that you have done exactly the right thing in adding your 'thank you' as a comment to the question to which it relates.
"Star of Bethlehem" is a 'common name' for the plant and the problem with common names is that the same name is often applied to a number of different plants - especialy by people living in different parts of the country or in different countries. Your wife's plant may well be correctly called Star of Bethlehem, as will be several other plants.
For me, Star of Bethlehem is a different Ornithogalum to the one in your picture even though that is right for Seaburngirl. I would nominate Ornithogalum umbellatum for the title; this has white flowers in an umbel at the top of the stem.
Scientific names may sound clumsy but each name applies to one specific plant only and, therfore, they remove a lot of confusion.

Bulbaholic suggests that the plant that appeared in our "plot" looks like the bulb Ornitholagum mutans. If it has grown from a bulb is it likely that the bulb could have arrived on the feet of a bird as it is not one that we have planted. Also, if the flowers do produce seeds will they produce other plants if planted?

More likely a seed was brought in, Fpm, I have not heard of birds carrying actual bulbs around. If it sets seed then, yes, these will produce new bulbs in time. Fully grown bulbs will be readily available from the garden center in a couple of months time, not expensive.