Thanks for your patience. Your only way to challenge this would indeed be through claiming constructive dismissal. This can be a tough claim though as the burden of proof is entirely on you to show that there was a serious enough breach to justify that.
In a TUPE situation you can expect to transfer to the new employer with your existing terms and conditions remaining intact, so it would be a claim that this right has been breached that would prompt constructive dismissal.
Another important consideration is that in such a claim you are mainly compensated for your loss of earnings from having to leave. Therefore, if you find a new job soon enough (which you are expected to consistently try to do), these losses will be greatly reduced and may make the prospect of making a claim somewhat pointless.
In terms of voicing your concerns over this, you can do this directly to the new employer but as you are nit their employee yet you will not be able to force them to deal with this or address it in any way. You will have to wait until the move has taken place and the changes have taken place to do so.
Please take a quick second to leave a positive rating for the service so far by selecting 3, 4 or 5 stars above. I can continue answering follow up questions and in particular can also discuss the steps you need to follow if you were to initiate the claims process. There is no extra cost for this - leaving your rating now will not close the question and means we can still continue this discussion. Thank you