It's very odd - the old website was replaced by the 'new' one by Kout when they bought Little Chef, but it's never been updated since it launched. The domain was re-registered on 08/08/2020, so someone is definitely still paying for it.Interestingly, the Little Chef website is still all there, up and running!
Home | Little Chef
www.littlechef.co.uk
As I understand it, Kout bought the brand and operations but then sold on the operations only to EuroGarages. I think they paid Kout around £2m per year to licence the brand, but they obviously decided it wasn't worth it and remaining restaurants lost any 'Little Chef' branding but continued as 'EG Diner' without any replacement signage until they got round to converting them all to Greggs/Burger King/Starbucks/Sainsbury's Local. The brand is still owned by Kout, with the intention of licencing it out again. A company a friend ran was interested in taking the brand on, but Kout refused to consider a sale and instead wanted several million to licence the brand to them.
It's a shame - I was always a fan of them, but unfortunately they just didn't move with the times.
Personally I think it's useful having brands on services signs, I tend to choose where I stop based on what's on offer.