In simple terms you look at the business as a whole
At the moment
You and other employees work for Joe's Shop
You turn up do the individual roles and get a payslip from Joe's Shop not Joe
Joe sells to Jill
You and other employees work still for Joe's Shop
You turn up and still do the individual roles and get a payslip from Joe's Shop
So it is the same business, your role remains the same and the only difference is who has authority to pay money from the bank accounts
So if Jill want a 40 hour employee she is making your 24 role redundant and creating a new role. She can do this but has to follow the same process that Joe would have had to follow because your employer is Joe's Shop (after being TUPEed your lenght of service covers both jobs)
Jill can move where you work either by you agreeing to change the specific work location in your contract or by a generic need of the business. Forcing you to change location can be constructive dismissal but if the rest of the business reason is vaild it is usually based around a reasonable geographical location between the two work locations not simply your home to work travel arrangements or your caring obligations.
In a TUPE situation Jill will buy all of the business except for the business name (legal framework).
You and other employees dont work for Joe's Shop any more, you work for Jill's Shop
However you still turn up and still do the individual roles only now you get a payslip from Jill's Shop
So it is the same business your role remains the same.
your role is still there so you cant be paid redundancy if you leave you are chosing to leave your 24h job.
One of the business assets Jill bought is your contract of employment as it provides an employee to do your role.
Your new employer has bought the employer rights (you provide your time/skill) and obligations (Jill provides pay and benefits except for pensions) listed your employment contract plus policy plus the unwritten /verbal agreements which developed through work pratice.
the trickey bit will be the unwritten bits so you need to go through what is written into your contract and what is only company policy or work pratice.
If you and the other employees are on better pay and conditions a new owner (Jill) could engage in sharp pratice to slowly change the policy which is an indirect change to your contract before transferring you to Jill's Shop.
If you and the other employees are worried (and can pool the fee) it you could hire an employment specialist to go over the contracts to see what could be added to ensure the policy benefits move with you as a contract obligation