Mr Appleton's appointment, which becomes effective 15 April, will enable him to work with Mr Mescall before he takes over running of the division later on this year.
Travis Perkins is one of the UK's biggest builders' merchants chains.
Mr Appleton has also been proposed as a non-executive, part-time director of Nordic rental company Ramirent. He continues to serve as a board member of the European Rental Association.
Lavendon Group plc is a leader in the rental of powered aerial work platforms in both western Europe and the Gulf States.