I have read that river names are some of the oldest names in the UK. Thames is believed to be from a pre-celtic language, apparently with a meaning of 'dark'. Ouse, Nene and others may also be pre-Celtic.

As for Pictish,I recently read a book on the Picts which showed a distribution of Pictish (mostly Eastern Scotland) and Gaelic (Western) place names. Unfortunately little is known of the Pictish language, although it was Celtic and survived until about 600AD.