There is a lemon oregano, and that plant certainly looks like oregano.

Can you move it outside? It needs fresh air and light.

Mystery solved! It is wild marjoram, Origanum vulgare 'Compactum', so not as aromatic or flavoured as Greek oregano or sweet marjoram. I can't move it outside as we don't have a garden but I'll see how it does on the windowsill... Thanks for the suggestions!

Does the container have drainage holes? Origanum vulgare is native to the British Isles and grows on thin, sunny well drained soils. It needs lots of light and not much water. Indoors conditions will be a challenge for it.

It has pebbles at the bottom at the moment for drainage, but I'll move it out of that pot anyway and put it in one that has holes at the bottom. I will probably have to give it away to someone who has a garden but I will look after it for now! Thanks!