This should probably be handled under TUPE — The Transfer of Undertakings (Protection of Employment) Regulations 2006 as amended by The Collective Redundancies and Transfer of Undertakings (Protection of Employment) (Amendment) Regulations 2014. Those regulations apply to "a transfer of an undertaking, business or part of an undertaking or business situated immediately before the transfer in the United Kingdom to another person where there is a transfer of an economic entity which retains its identity"
Broadly, there must be some consultation but you cannot be forced to change the terms of your contract to your material detriment (for example, the date of the month you are paid might change, but your work and salary would not). This consultation should establish that there is no material detriment (carry on reading here). Regulation 13 provides
(2) Long enough before a relevant transfer to enable the employer of any affected employees to consult the appropriate representatives of any affected employees, the employer shall inform those representatives of—
(a) the fact that the transfer is to take place, the date or proposed date of the transfer and the reasons for it;
(b) the legal, economic and social implications of the transfer for any affected employees;
(c) the measures which he envisages he will, in connection with the transfer, take in relation to any affected employees or, if he envisages that no measures will be so taken, that fact; and
(d) if the employer is the transferor, the measures, in connection with the transfer, which he envisages the transferee will take in relation to any affected employees who will become employees of the transferee after the transfer by virtue of regulation 4 or, if he envisages that no measures will be so taken, that fact.
(6) An employer of an affected employee who envisages that he will take measures in relation to an affected employee, in connection with the relevant transfer, shall consult the appropriate representatives of that employee with a view to seeking their agreement to the intended measures.
If you refuse to accept the transfer you are deemed to have resigned (Regulation 4(8)), unless the "transfer involves or would involve a substantial change in working conditions to [your] material detriment", where you can be deemed to have been dismissed (Regulation 4(9)), and potentially unfairly dismissed. That would be for an Employment Tribunal to decide. But you cannot exit the successor company except in accord with your contract, including any notice period.
The 2014 amended Regulations deal principally with the issue of redundancy after transfer, which is specifically allowed for "economic, technical or organisational reasons", such as the new company deciding to rationalise operations in a location 300 miles away from your normal base. In those circumstances you can be made redundant if you don't move with your job or accept redeployment. [This is what happened to me.]
Note that every TUPE transfer is unique, and while yours will be subject to the Regulations, the wrinkles in your particular case (a) aren't present in your question and (b) will best be answered by a specialist employment lawyer, particularly as to whether any necessary changes to your contract are to your "material detriment".