Cook has particular expertise in high-value corporate real estate transactions. Last month she and Peña worked on the £460m refinancing of Kandahar Real Estate for Bank of Scotland.
Clifford Chance global head of real estate Cliff McAuley said: "Catherine's a very good fit with our practice, both in terms of culture and experience."
A BLP spokesman said the firm wished Cook well and that the team looked forward to partner Chris De Pury's arrival from Herbert Smith. De Pury came to an agreement with Herbert Smith last week and will leave for J Sainsbury bidder Three Delta immediately and join BLP in January.