There are many factors which determine the suitability of a job. No one specifically decides if it is suitable but it is an objective thing. If there is a disagreement then only a tribunal can determine the final answer and if it is something which should be deemed suitable or not. The most common factors are:
• Job content/status – drop in status, substantial changes in duties, etc.
• Pay and other benefits – significant drop in earnings/benefits (e.g. basic pay, bonuses, overtime, sick pay, holidays)
• Working hours – change in shift pattern, removal of overtime, extension/reduction of working hours
• Change of workplace – new location making it unreasonable to travel to the new place of work
• Job prospects – going from permanent to temporary work, becoming self-employed or being employed on a fixed-term contract.
They can reject redundancy for any reason – they cannot be forced to make you redundant so if they decide that you will have to either accept it or resign and claim constructive dismissal instead. The trial period you mentioned only applies to actual redundancy situations, not when there is just a change in role or following TUPE so you cannot rely on that here.
Your main argument here is the changes to your role following a TUPE transfer. Under Regulation 4(4) of TUPE any such changes are automatically void, unless the employer can show they were in no way connected to the transfer or if they were necessary for an economic, technical or organisational reason (ETO reason) subject to employee agreement or the terms of the contract permitting the change.
Some employers may try and justify changes by arguing that they are needed due to harmonisation and therefore rely on an ETO reason. However, Government guidance and case law has restricted the application of harmonisation as a genuine reason to amend a person's terms of employment. Harmonisation will only be a valid reason if there is a change in the workforce and this must involve change in the numbers, or possibly functions, of the employees. In practice, relatively few contractual changes would involve such changes so harmonisation will rarely be used as a justifiable reason.
If the changes are part of a wider reorganisation which has nothing to do with the transfer, then they may be effective. The longer the gap between the TUPE transfer and any reorganisation, the greater the chance that the causal connection will be broken. However, there is no specific period after which it is safe to say that the connection with the TUPE transfer has been broken, as the test is whether the change is connected to the transfer. The mere passing of time does not of itself break the connection.
It is for the employer to prove that a proposed change is permissible under TUPE and if there are concerns that the changes cannot be made, this can be challenged by raising a formal grievance first and then considering making a claim in an employment tribunal as discussed. Hope this clarifies things for you a bit more?