Yes — you have the legal right to object to transferring to the new employer. But if you object, your employment ends automatically on the transfer date: no redundancy pay, no notice pay, and normally no unfair dismissal claim. Objecting is effectively resigning without notice pay.
If the transfer involves a substantial change to your working conditions to your material detriment — such as a significant relocation or demotion — you can treat yourself as dismissed and may still claim unfair dismissal. Always take advice before resigning.
If you genuinely don't want to move to the new employer, negotiating a settlement agreement before the transfer is almost always better than objecting.