Yes. Calling in sick during your notice period works exactly the same as any other time. You're entitled to statutory sick pay (or contractual sick pay if your scheme is more generous), the absence counts toward your notice as normal, and your final working day doesn't move. Employers are usually more sensitive to sickness during notice for obvious reasons, but the rules don't change.
The legal position is simple: the notice period runs whether you're at work, on holiday, on garden leave, or off sick. Days you spend at home unwell are notice days the same as any other. Your employment ends on the same date it would have if you'd worked every day. If you exhaust your notice while off sick, your employment ends on the scheduled date and you're paid your normal entitlements up to that point.
Statutory sick pay (SSP) applies if you've been off for four or more days in a row (including non-working days) and you meet the earnings threshold. SSP runs to a maximum of 28 weeks, which is longer than any normal notice period, so SSP coverage is rarely the limit. Contractual sick pay schemes (often called 'company sick pay') sit on top of SSP and can be more generous; check the policy.
Sick pay during notice can be more nuanced if your contractual scheme limits enhanced sick pay to active employees in good standing. Some schemes pause or reduce contractual sick pay during notice periods. The wording is usually obscure. The statutory minimum (SSP at the daily rate, where eligible) always applies; the question is whether the company's better scheme kicks in. Read the sickness clause if you can find it.
If you're genuinely unwell, the usual processes apply: notify your manager on the first day of absence, follow whatever the company's reporting policy is, and get a Statement of Fitness for Work ('fit note') from your GP if the absence runs beyond seven calendar days. Failure to follow the policy can sometimes affect sick pay, but not your underlying entitlement to be off if you're genuinely unable to work.
Employers occasionally suspect that notice-period sickness isn't genuine. They have the right to question repeated short-term absences, and they can ask you to attend an occupational health assessment if there's a pattern. They can't refuse to accept a fit note from your GP, but they can challenge the underlying picture. As long as you're genuinely ill, the right paperwork and the right process keep you protected.
The handover question is the one that creates friction. If you're off for a week of your two-week notice, the employer has lost half the handover time they expected. Some employers ask whether you can do email or remote work to keep things ticking; you don't have to agree if you're not well enough, and you shouldn't pretend you are. Some will offer to extend the notice; you don't have to agree to that either.
If you genuinely can't work the notice because of illness and the employer wants you out sooner, PILON for the unworked portion is the clean solution if their contract allows it. The result is the same financially; your employment ends earlier rather than running to the original end date. Make sure any agreement to switch to PILON is in writing so the date and amount are documented.
General information about UK employment law. For your specific situation, contact ACAS or an employment-law solicitor.