Can transferring staff rely on TUPE to ask for better benefits?

No. TUPE protects the transferred employee’s existing employment rights. It does not improve on them. For example, in Jackson v Computershare Investor Services plc [2007] EWCA Civ 1065, an employee transferred into a business whose existing employees benefited from an enhanced redundancy scheme. After being made redundant, Ms Jackson was refused the enhanced redundancy package, because it had never been a part of her employment contract with her old employer. This was not a breach of TUPE.