story identification - Trying to recall series of novels set in palaeolithic Europe with time travel from near present

I read this series in the 80s I think. It was set in the Stone Age or earlier.

There was the usual disparate band of youngsters but who had time travelled from the near future. Think there was a reality show theme to it. One or more had increasing telekinetic powers.

The climax of one of the books was a was the breaching of a the straits of Gibraltar leading to the formation of the Mediterranean.

Answer

As mentioned by @eshier this the Saga of Pliocene Exile by Julian May

The Saga of Pliocene Exile (or the Saga of the Exiles) is a series of science / speculative fiction books by Julian May, first published in the early 1980s. It consists of four books: The Many Colored Land, The Golden Torc, The Nonborn King and The Adversary.

At the start of the story the Strait of Gibraltar is closed and the Mediterranean Sea is dry and empty. The Many Colored Land and The Golden Torc are set in Europe just before and during the rupture at Gibraltar.

The rupture and the rapid filling of the Mediterranean form a Wagnerian climax to The Golden Torc, in which aliens and time-traveling humans are caught up in this cataclysm.

The Saga of Pliocene Exile (known as the Saga of the Exiles in some markets) is a narrative surrounding the adventures of a group of late 21st and early 22nd century misfits/outcasts who travel through a one-way time-gate to Earth's Pliocene epoch, in the hopes of finding a simple utopia where they can escape the complexity and politics of the modern post-intervention intergalactic society.