In this context, it's important to differentiate between circles / rings (frog eyes) and dead spots or patches, and a photo would help.
As for rings-
1) fairy rings: with or without mushrooms
2) necrotic ring spot (Also a fungus issue)
3) 'summer patch' rings (also fungus)
In the U.S., I would contact my local university agricultural extension service (not lawncare people) for information on diagnostic testing a turf sample for a positive diagnosis. This will point to the best treatment options, as fungus issues are tough and expensive and sometimes need a specific treatment. Does the U.K. have a similar local agricultural department associated with the university system?
You may know this, look these problems up using EDU as a preface in your search to point you towards university sources instead of lesser quality 'rebloggers' trying to profit from your clicks or sell you a miracle cure. This works because universities have the .edu suffix in their URL. U.K. university sources may be more helpful to you.
Search string:
'EDU necrotic ring spot'
Or
'EDU fairy ring in grass'
Or
'Edu circles in grass'
Grub or soil bug damage is also a possibility. Dig up some grass at the border of the ring to look for grubs or insects or damage in the roots.
I would far prefer to find grubs or bugs as they seem easier to control than stubborn fungus issues.
Good luck.
