Gabriel Diya, 52, his daughter Comfort Diya, nine, and his son Praise-Emmanuel Diya, 16, were named as the tourists who died at the Club La Costa World complex in Spain on Christmas Eve.
Mr Diya, who was a Christian pastor in south-east London, and his daughter are both understood to be British while his son was travelling on a US passport.
His wife Olubunmi Diya, 49, and younger daughter Favour Diya, 14, were also on the holiday but were unharmed.
On Thursday they told investigators that none of their relatives could properly swim and only nine-year-old Comfort had 'some idea'.
It is feared that the family could have fallen victim to a suction problem which made it impossible for the nine-year-old girl's father and brother to rescue her after she got into difficulties at the resort near Fuengirola.
It was revealed that police divers had found her swimming cap as they investigate the Christmas tragedy.
But the exact circumstances of their deaths remained a mystery this morning as resort chiefs said they had been given permission to reopen the pool and insisted a police investigation had found 'no concerns' with it.
Mr Diya, who also ran his own property business, was a pastor at Open Heavens London in Charlton, south-east London, which is part of a network called the Redeemed Christian Church of God.
It is part of the Redeemed Christian Church of God, which posted in tribute on Facebook: 'With heavy hearts, we extend our condolences to the family, parish, friends and associates of Area Pastor Gabriel Diya who sadly passed away, along with two of his children ... in a tragic incident while on a family holiday in Spain.
'At this very difficult time, our prayers are for Pastor Gabriel Diya's family, the parishes that were under his supervision, friends, associates, members of RCCG and the general public.'
A neighbour of the family told the PA news agency she was 'really devastated' to learn of the deaths, describing the Diyas as 'very religious, very friendly, very humble'.
Speaking outside her home in Charlton, south-east London, Lara Akins, 59, added: 'I still can't comprehend it, it's still shocking.
'They are so nice, that is why everybody is shocked... we are very friendly with each other.'
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