A peer in Britain is someone with a title (Baron or higher). Some are hereditary but most are not (these are called 'life peers'). All life peers and some hereditary peers sit in the House of Lords, one of two houses of parliament in Britain. Many peers who sit in the House of Lords (but not all) are members of and align themselves to a political party. These often are often referred to as [party name] peers. Peers who are not members of a party are sometimes referred to as 'cross-bench peers'.
Lord Mendelsohn is a member of the Labour Party who sits in the House of Lords.