I think you might lose more paying a solicitor than for any compo you would get.
(As an example, with the recent data breaches I don't anyone whose details leaked to criminals will get compensation unless they're actually at a loss - and even then, it might be just enough to cover their financial loss - this despite their details being known to criminal actively seeking to defraud them)(of course I could be wrong on all this - not an expert in this area)