Researchers have estimated that the current warm weather may have caused up to 760 premature deaths in Britain.
Health officials have advised people to stay cool, drink lots of cold fluids and keep an eye on those they know to be at risk.
Dr Angie Bone, heatwave plan leader for Public Health England, said that high temperatures can be dangerous, especially for people who may be vulnerable such as older people, young children and those with serious illnesses.
Meanwhile, a high temperature warning remains in place for Ireland.
Met Éireann says temperatures will reach values between 27C and 30C in many areas today and tomorrow.
It forecasts that the very warm and humid weather will continue next week.
In Britain, a four-week-old baby was among ten children admitted to one hospital in the southeast with sunburn since the period of hot weather began.
Six of the children admitted needed specialist treatment after being referred to the unit from other hospitals because of the severity of their burns.
A spokesman for the hospital said the extent of the burns ranged from 0.5% to 4% of the body surface area.
Consultant plastic surgeon Nora Nugent said: "The sun at this time of year is very strong and children can get burnt very quickly.
"The children we've treated over the last few weeks have been referred to our unit because their burns have been so severe they have required specialist treatment."
Doctors in Wales warned of the dangers of ride-on lawn mowers after seeing plastic surgery trauma cases double to 53.
Dean Boyce, consultant plastic surgeon at the Welsh Centre for Burns and Plastic Surgery at Morriston Hospital in Swansea, said: "Unfortunately we are treating a patient with a very severe foot injury, and this is not the first time this has happened.
"We have seen children who have lost a foot after falling off a parent's lap riding a ride-on mower."