No, but if you refuse to transfer (known in the TUPE regulations as 'objecting to the transfer'), your rights are very limited.
You may be able to negotiate a new contract with your employer that allows you to remain with your employer but in a completely new role, outside the pool of transferring employees. But if you remain inside the pool of transferring employees on the transfer date, your employment will transfer automatically to the new employer, unless you have objected before the transfer. This is a very complicated area of law. Take advice as soon as possible if you are in this position.
If you object to the transfer before the transfer date, your contract of employment will come to an end and you will be treated as having effectively resigned. You will not be able to claim a redundancy payment.
You may be able to claim unfair dismissal, but only if you can demonstrate that the transfer has resulted or will result in a substantial worsening of your working conditions.
TUPE is very complicated. It is very important that you and your colleagues take advice from your union rep as early as possible.