At times, one in four adverts shown before and during the programme on ITV Hub were for food and drink high in fat, salt and sugar (HFSS), according to analysis by the Obesity Health Alliance.
The coalition group has called for a 9pm watershed to protect children from junk food marketing and said restrictions should also apply to programmes viewed using on-demand services.
Caroline Cerny, from the Obesity Health Alliance, said: "It is hugely concerning that children could be exposed to so many junk food adverts wherever they watch their favourite shows - be it on live TV or on-demand services.
"We know that the Britain's Got Talent final was the most watched programme by children in 2017, and with this year's final broadcast live until 9.30pm on a Sunday night, it is highly likely that many kids will have caught up with it the following day or after on-demand.
"The Obesity Health Alliance is calling on Government to restrict junk food marketing restrictions with a 9pm watershed on TV.
"Our analysis reveals that any restrictions placed on TV advertising should also apply to on-demand services, so that parents can rest assured that their children will not be exposed to harmful junk food advertising whenever, and wherever, they watch the shows they love most."
The researchers analysed adverts shown while watching the Britain's Got Talent final online in three separate sessions, after it was first broadcast on ITV on June 3.
They used their own ITV Hub accounts, which identified them as over-18s.
In the first session, nine out of 42 adverts were for HFSS products, while in the second, 11 out of 42 adverts were for unhealthy foods including burgers, pizza and sugary drinks.
When parental controls were switched on, and the programme was viewed using a Smart TV, four out of 35 adverts were for HFSS products.
During one viewing session, McDonald's adverts were broadcast in half of all the breaks, the researchers said.
Dr Max Davie, officer for health promotion for the Royal College of Paediatrics and Child Health, said: "Food manufacturers market their products at children because they know it leads to an increase in sales.
"However with one in three children overweight or obese by the time they start secondary school, and advertising being one of the contributing causes, it is only right that a ban on advertising of products high in salt, sugar and fat, is put in place before 9pm on television and for on-demand broadcasts regardless of the time they watch."
Around half of eight to 11-year-olds and two thirds of 12 to 15-year-olds regularly watch TV on other devices, the Obesity Health Alliance said.
It is likely that children are watching shows on catch-up services, using family or their parents' accounts, the group suggests.
The calls for tighter junk food advertising restrictions come ahead of the next chapter of the Government's Childhood Obesity Strategy.