I know that the Travelodge chain of hotels in some regions of the world is part of the Wyndham Rewards programme. However, I'm not quite sure whether the UK chain (it doesn't seem to be affiliated with the main brand) is part of any loyalty programme. Is it?
No, it isn't part of any of the big hotel chains. That's partly why it's so cheap. That means no credit to any loyalty programs you might be a member of, sorry.
Travelodge UK doesn't have its own loyalty program either. All they have is business discounts and billing.