It's Dracaena deremensis, 'Janet Craig', assuming it has no longitudinal stripes of a different shade, which is diffcult to tell from the photo - I can see what might be either shininess or a stripe. If it does have a variegation, its still Dracaena deremensis, just a different variety. It's certainly liking its situation.

I am just slightly querying your answer Bamboo as I have found pictures of Janet Craig on the internet and the leaves of these appear to grow in clusters at the top of the stems whereas mine has leaves growing all the way up the stems, alternately, with about an inch between each node. I am wanting to cut it back a little as it is just about up to our ceiling but I'm not sure whereabouts I should cut and will it survive if I do? The leaves certainly look very much like a Dracaena though.

Dracaenas are, by and large, 'cane' plants, which means you can grow or buy them as a thick cane with growth sprouting from the top, which is probably what the picture you saw was showing. Sold in this form, they're often called Ti trees. I have Dracaena deremensis 'warneckii', bought when it was small, and it's grown like yours, with leaves all the way up the stem. Well, except I forgot to water and now the lower 2 sets of leaves are withering...

Cane cuttings can be taken, but the cane is usually very mature (looks pale brown) as you can see on yours, at the base. I don't know what will happen if you cut yours, but I'm pretty sure it will be just fine, branch out and grow upwards again.Yours has been cut at some point, because they usually grow on a single stem, and yours has two, so if its getting too tall, I'd cut off half the top growth, maybe more, and let it grow on again. Bear in mind, though, that where you've cut, it will produce 2 stems, maybe more, from that point onwards, and that consideration might make a difference as to precisely where you do cut. If you're anxious about cutting it, just cut one stem down and see what happens. You could even try rooting what you cut off by using the top 6 to 8 inches, strip off the lower leaves leaving the top 2 or 3, and pop in a bottle of water so its suspended. Leave it on a windowsill and it might root - it works with other plants, but I've never tried it with Dracaena.

If you're still unsure about the identity of this plant, I can always post a picture of mine, although of course mine is striped, but it will at least confirm that it has leaves all the way up the stem. Let me know if you want me to do that.

Thank you very much for your kind offer, Bamboo, but I'm sure you're right about mine being a Dracaena. Your help with regard to cutting back is very much appreciated too. I'll try cutting back one stem and see how we go. Will let you know but it could be some time from now, obviously!

The leaves look a little too smooth for a Dracaena deremensis variety to me--that species has prominent parallel veins on its leaves. I'm thinking maybe a D. fragrans, or one of the newer hybrids. As for leaves all the way down the stem, that is a sign of good care, though it might be able to use a little more light, judging by the internode length.

Apparently Dracaena Fragrans is a flowering form and, although I have had this plant for around 5 years, it has never flowered. I must admit, however, that the leaves appear identical.

Blimey Tugbrethil, your sight must be infinitely better than mine - I can't tell whether this one has veining or not. I can't honestly say my plant has particularly prominent veining though...
Either way, it should respond fine to cutting, Terrna

I have changed the picture now so that you can see a close-up of an individual leaf. It is very smooth and shiny with no ridges or coloured stripes.

Yes, Terrna, definitely D. fragrans, which may never bloom indoors, particularly in low light conditions, which yours looks to be in. Even if it does bloom, I haven't often seen it on plants less than 7 years old.
Bamboo, I blame decades of trying to identify plants from blurry Polaroids or I-phone shots!! :D

Many thanks to both those people who offered me advice. I hope to be acting on this in the Spring.