I think the author you're thinking of is David Hutchinson. He uses the term "gates" for teleportation devices. He called the process "transplacement".
He wrote short stories under that name in the late 1970s/early 1980s. Then, after a long break from writing, he switched to the name Dave Hutchinson.
In particular, in his third short story collection, Torn Air, there is a short story called Abyss which is about a man wandering through a deserted Britain. The book was published in 1980 which matches your timeline. This story has two features that make me think it's one of the stories you're after.
Firstly, it describes the invention of transplacement in a way that would tally with your description of it as a discovery:
Ray Preston had stumbled on transplacement as a theoretical possibility while working on the strange structure of elementary particles. It was one of those strange scientific sidesteps that only happen very rarely, and Preston, though never doubting the validity of his theory, could never understand how it worked at all.
Secondly, it also describes the spread of diseases:
The World Health Organisation had tried to delay the introduction of gates several times at the United Nations, and each time it had been overruled. The advantages outweighed the disadvantages, so long as people were careful. People weren't careful, as usual. Transplacement could spread typhoid from Calcutta to Croydon in the time it took to dial four digits, then up to half a dozen more, then step through ...
If transplacement had come three years later, perhaps immunology whould have been ready for it; as it was, plagues started in one place, then erupted in another, perhaps a thousand miles away. It was impossible to stop once it had begun. Soon there weren't enough people to try...
If it helps you remember, the gates are describe in a manner to telephone boxes. At least you select your destination by punching a number into a push-button telephone dial:
... a skeleton gateway of square-section metal tubing, a little more than a man high and two men wide. Attached ... was a square push-button telephone dial ...
You could dial anywhere in Britain with six digits ... He punched six random digits, waited for the little light to go on, and flicked a twig through the gate.
It vanished without a flicker.
A quick search should find a picture of the book. It has a distinctive cover which might jog your memory.
As far as I can tell, David Hutchinson's early work, including Torn Air, is out of print, which is a shame.
Torn Air has ISBN 0-200-72691-9. It was published by Abelard-Schuman Limited.
