Yes. Probation is just a contractual arrangement at the start of a new job; either side can end it by giving the contractual notice (often one week, sometimes longer). You don't need permission to resign during probation, and you don't need to explain yourself. Hand in your notice in the normal way and serve out whatever your contract specifies.
Probation isn't a separate legal status. UK law has no statutory probationary period; it's entirely a creation of your employment contract. That means resigning during probation works exactly the same way as resigning at any other point. You hand in written notice, you serve the contractual notice period (or take PILON if your employer offers it), and your employment ends on the last day of that period.
The notice you have to give during probation is usually shorter than after probation. One week is common; some contracts specify the same notice as post-probation, others reduce it as low as the statutory floor (one week from one month of service, nothing before that). Whichever figure your contract gives, that's what applies. Check the notice clause specifically; it's almost always called out separately for probation.
What you give up by leaving during probation is mostly time. The big employment protections in the UK kick in at length-of-service thresholds rather than at the end of probation. Ordinary unfair-dismissal protection starts at two years of continuous service. Statutory redundancy pay starts at two years. Enhanced contractual benefits like longer notice, sick pay or pension matching often start at the end of probation, so leaving early means you walk away from those.
Practically, the steps are the same as any resignation. Put it in writing, even if you also tell your manager verbally. Keep a copy with the date. Send it from your personal email or hand over a printed copy you've kept a record of. State your last working day calculated from the notice clause. You don't need to give a reason, but a sentence of context (the role isn't a fit, you've had another offer, personal circumstances) keeps the conversation civil.
Some people worry that resigning during probation looks bad on future CVs. It depends on what comes next. A short stint that's clearly a deliberate move (to a better role, a different city, a different industry) reads fine. A pattern of multiple short stints in a row is harder to explain. Either way, no future employer can see your probation status; they can only see start and end dates.
If you're resigning because the role isn't working out and you're not sure where to go next, garden leave or PILON probably aren't on the table for a probation-period departure; employers reserve those for senior or competitive exits. You'll most likely work the notice. Use the time to wrap up tidily, hand over what you have, and leave on good terms. References from short stints still matter.
If something more serious is happening (the role was misrepresented, you're being treated badly, you've found you can't do the work safely), the same general advice applies but you may want to take advice from ACAS or a solicitor before resigning. Constructive dismissal claims need two years of service to bring an unfair-dismissal claim, but other routes (discrimination, breach of contract) don't have the same service threshold.
General information about UK employment law. For your specific situation, contact ACAS or an employment-law solicitor.