Wimpy was not alone, before McDonald's franchises were commonly available in the UK, there were many burger shops that sometimes operated as a small chain.

One survivor is Burger Star (best by far), which is now down to a single location, down from their peak of about four locations.

When McDonald's was not everywhere it was quite easy for local shops to offer an American dining experience because most people had never been to the USA or McDonald's. It was cultural appropriation of sorts. In the 1980s everything American was awesome in the imagination of British people, exactly like the movies with Disney theme parks as the ultimate. In these times anything American was more sophisticated, whether it was 501 Levis, Nike shoes, water beds and much else that we stereotyped.

Wimpy made no claim to be faux American, it was definitely very British. So I don't see a battle of the burgers. Wimpy went the way of Little Chef, another British food chain that just got stuck in the past. People just didn't want that sit down, waited on experience any more, they wanted take out, which was not something Wimpy was known for.