Your health is a private matter and you're not obliged to inform your employer about your diagnosis. However, cancer is treated as a disability under the Equality Act 2010, which means your employer will have additional duties and obligations towards you. This will include a legal duty to make reasonable adjustments, which may include allowing you time off work for treatment. However, if your employer doesn't know about your condition, or couldn’t reasonably be expected to know about it, then their duties under the Equality Act will not kick in.
Your employer can’t refuse you time off for treatment. However, you may not be entitled to paid time off – this will depend on the terms of your employment contract. Your employer may request (written) evidence about the diagnosis and details of time off needed for any treatment and recovery. Your doctor or treatment team should be able to provide this evidence.
If you are fit enough to do so you can return to work but if the medical advice is that you should have a phased return to work and/or possibly on reduced hours or duties this should be discussed with your employer as possible reasonable adjustments under the Equality Act