A Contract does exists -this is absolute.
Consider what your customary practices were before the changes and any other letters and meetings of agreements and write these down. Especially the working relationship between you and the former owners/employer, issues about payments & invoices etc., then to get an aspect of implied terms visit your local job centre's website, talk to Acas etc or more importantly a legal representative and this would give you a basis to evaluate and formulate previous agreed terms. (Acas should be sufficient if wanting to avoid legal costs at this stage but should not be overlooked).
Draft a specification of works done previously that the former client requested and your staff had been doing for a number of years. With this foundation compare what this new owners wants you to change. You can consider this process as your variation of contract stage and it is open to both parties to agree these new rules. Don't feel intimidated and that you have to comply with everything they say unless it is considered a reasonable request i.e. it relates to working standards, H&S etc. Once you have this if there are more works required than originally agreed then you need to consider talking about "increased pricing" for additional works.
Now, do not make the same mistake twice, get these clients to formulise a written contract with all new terms and pricing. Daily changes should not be allowed, however you can compromise where it relates to standards and remedial works need to take effect.
It is not exactly clear although asked by a member what paperwork is requested from you. It could be that they are more efficient than the former owners and need to comply with legislations, working practices etc. in which case this is a good thing but a head ache for you but benefits you in the end. This is the general way you should be heading or be at if operating for some time. I am causious that you appear to be running this contract without an agreement when a number of staff are also involved. Do you have agreements for other sites you're operating in? Why is there a request for timesheets? Are they paying your employees directly? What is the arrangement here? Surely you should be invoicing directly and on payment pay your own staff thus operating your own PAYE Scheme. This point needs clarification.
Assigning the timesheet management to your supervisior isn't a problem but you seem to indicate 'whatever you do is not right' what do you mean? Please give an example.
In reference to walking away from the contract you would need to consider the impacts of doing so. Yes you can give reasonable notice to terminate your contract with the new owners but the effects of this would as explained above impact on your employees. This includes dismissals and redundancies covering employees who have also worked for less than 2 years. Where you find you cannot relocate these employees if you were to terminate your contract before a new company takes over, such employees can only look to ET for remedies and if you stay until a new contractor takes over then TUPE will come into effect.
Its your business and yes some clients can be a challenge but try to find the mutual ground. Let then see you are in control of your business, skilled and know what you are doing. If they think you are a push over they will continue to make demands for which you will not be rewarded. You cannot be in a position to posibbly run a contract without making profits only servicing your clients needs and keeps employees in a job. You need to also obtain a monetary benefit from servicing this contract. If these changes are eating into your profit margins then you know what must be done.
I hope this helps and good luck