Along with nine deaths in the UK, the Gardai in Ireland also said a teenage girl died in the sea at Burrow Beach, a popular swimming spot near Howth, on Sunday.
The RNLI have warned of the “very real risk” of swimming in open water during the heatwave.
Visits to NHS web pages have also surged during the heatwaves as people sought advice on how to stay safe in the hot weather.
NHS England said there were 20,092 visits to its heatstroke advice page on bank holiday Monday, compared to just 488 the previous Monday. Over the whole weekend, there were 36,724 hits.
Elsewhere, people looking for tips on how to deal with sunburn led to 5,342 visits to NHS webpages, with a total of 10,314 over the whole weekend.
Parents also sought advice on how to keep their babies safe, with visits to NHS web pages for baby first aid and sun safety tips surging by almost 3,500% on Monday, with 4,728 hits.
While many people enjoyed the sunny bank holiday weekend, older people and babies can be particularly vulnerable.
There is also a risk of dehydration and heat exhaustion, which is caused by the body losing too much water and salt, and can lead to heatstroke, a life-threatening illness.
Temperatures are expected to cool slightly in parts of the UK in the coming days but health officials have confirmed that heat health alerts would be extended for 24 hours.
The UK Health Security Agency said amber alerts for the South West, South East, London, East and West Midlands and the East of England will remain in place until 5pm on Thursday, with yellow heat-health alerts for the North West and North East.
The Met office have also issued a yellow thunderstorm warning for much of Wales, the South West of England and parts of the Midlands for 3pm to 11.59pm on Wednesday.
The warning stretches from Plymouth up to Holyhead and could bring torrential downpours of rain, frequent lightning, large hail and strong, gusty winds.