You’re an employee
A person is an employee if they are engaged under a “contract of service” rather than a “contract for service”. The distinction in the common law dates from the 19th century when industrialisation created more and more employees and those employees slowly gained more and more rights.
Legislation in the UK (and most other common law jurisdictions) does not usually further define employee so the common law definition is still relevant. The Copyright, Designs and Patents Act 1988 is no different.
The courts have developed 3 tests to determine if a person is subject to a contract of service. These were stated by MacKenna J in Ready Mixed Concrete (SE) Ltd v Minster of Pensions and National Insurance  2 QB 497
A contract of service exists if these three conditions are fulfilled. (i) The servant agrees that, in consideration of a wage or other remuneration, he will provide his own work and skill in the performance of some service for his master. (ii) He agrees, expressly or impliedly, that in the performance of that service he will be subject to the other's control in a sufficient degree to make that other master. (iii) The other provisions of the contract are consistent with its being a contract of service.
These are known as the control test; the integration test; and the multiple test. It is now considered that the control test and the integration test (which were both developed first) are now merely factors, albeit significant factors, of a single multiple test.
I can put the point which I am making in other words. An obligation to do work subject to the other party's control is a necessary, though not always a sufficient, condition of a contract of service. If the provisions of the contract as a whole are inconsistent with its being a contract of service, it will be some other kind of contract, and the person doing the work will not be a servant. The judge's task is to classify the contract (a task like that of distinguishing a contract of sale from one of work and labour). He may, in performing it, take into account other matters besides control.
The definition is a little tautological: a contract is a contract of service if it has the elements of a contract of service. This case was also important as it clearly establishes that whether a contract is an employment contract is a matter of law and the parties cannot redefine their relationship with words - if it meets the requirements of a contract of service then that’s what it is even if it describes itself as something else. A duck test is required.
The sorts of questions that are relevant to the multiple test are:
- Can you work whatever hours you like?
- Can you work where you like?
- Do you get paid for what you produce (rather than by the hour or day)?
- Can you hire somebody else to do the work?
- Do you have to fix defective work without additional pay?
- Can you make a profit or loss?
- Can you be sued if you screw up the work?
- Do you use your own plant and equipment?
- Do you carry your own public risk/professional indemnity insurance?
- Do you provide services to multiple clients and can you choose the quality of service you give to each?
From your description, the “agency” sounds exactly like a labour hire employer. The fact that you can pass on individual placements is not enough to make this a contract for service since, if you do accept the placement, you can’t send me to do the work, you can choose to work from 6-10 in the morning and 6-10 in the evening 4 days per week, you get paid by the hour etc. This is a contract of service and the agency is your employer. Any copyright you create belongs to them. It is likely that their contract with their client assigns it to the client but that is of no interest to you.