I'm not a member of the GW team, and I don't know.
One might say that the distinctive colour and typeface of the Gardener's World logo form a brand identification, and are some form of intellectual property. In your question, you recognise that because you refer to the image as a 'logo'.
But I can't understand what reason anyone would have for wanting to use the Gardeners' World logo on their website.
It wouldn't make sense to say, for example, that you are helping to advertise Gardeners' World. Far more people know about GW, and visit this site, than visit yours.
So why bother?