The bodies of Bonheur Musungay, 14, and Stella Kambi, 17, were recovered from the water at Thorpe Marshes Reserve near Norwich on Wednesday evening.
Police said they were "close friends" who had been out with a family group.
Norfolk Wildlife Trust said vandalised "no swimming" signs at the site had only been replaced two days before.
Emergency services and search teams were called at about 16:50 BST and the children's bodies were recovered at about 19:20 BST.
Norfolk Police said inquiries were continuing and post-mortem examinations would be carried out.
Det Sgt Sarah Knights said: "Without wanting to pre-judge what has happened, I would urge people to take the utmost care around water and to be aware of hidden dangers such as fast-flowing currents and underwater obstacles and weeds."
One girl, who was visiting the site at Thorpe St Andrew with her father earlier, said the lake was a "popular swimming spot".
"Often kids from school will come down here and come back with wet hair," she told the BBC.
Norfolk Wildlife Trust said it had had ongoing problems with its "no swimming" warning signs being destroyed and had replaced three sets in a year.
On 21 July, five signs were put at the reserve entrance and on the bank and in the water where people were known to swim, but they had all disappeared by 6 August.
By Monday, two new ones were put at the entrance and one in the water and trust chief executive Brendon Joyce said they were still in place.
"Our first thoughts are with the family and friends of the two teenagers," he said.
"We are unclear as to exactly what took place that led to such very sad circumstances."
He said that in response to the repeated vandalism they have been trying different signs and locations for them at the lake.
"We [also] have a much larger vandal-proof sign being produced which features safety warnings and general information about the reserve, but we're not sure where we're going to put it at the moment."
Mr Joyce said the "do not swim" warning was also on its website.
Two teenagers who died after getting into difficulties in a lake at a wildlife reserve in Norfolk have been named by police.