No. Resignation is a unilateral act in UK employment law. Once you've given valid notice in the right form, your employment will end at the end of that notice period whether the employer accepts it or not. There's no acceptance step. The only thing an employer can change is what happens during the notice period itself, not whether it ends.
Resignation works like this: you give notice in the form your contract requires (almost always written), the notice period runs, and on the last day of that period your employment ends. The employer doesn't have to agree, sign anything, or acknowledge it. Their reaction is socially important and useful to manage, but legally it doesn't matter. If you've given valid notice, you're going.
What employers actually mean when they say they're not accepting a resignation is usually one of three things. They want you to reconsider and stay, in which case they're starting a conversation rather than blocking you. They want to negotiate the leaving date, which is fair to discuss. Or they're trying to intimidate you into withdrawing, which is the one to be careful about; it doesn't have legal force.
There is one circumstance where 'rejection' has meaning: heat-of-the-moment resignations. If you've resigned in anger and immediately regret it, your employer can refuse to treat it as a resignation and let you carry on. The case law treats spoken-in-anger resignations as ambiguous; a reasonable employer would check that the person really means it. If you've calmed down and want to stay, ask within a day or two while it's still fresh, and put your retraction in writing.
Once written notice has been given and acted on (handed over, emailed, formally acknowledged), the position flips. You can ask to withdraw, but the employer doesn't have to agree. Many will accept a quick retraction; others won't, particularly if they've already started planning the handover or briefed the team. There's no legal right to undo it. So if you might want to back out, give yourself a thinking gap before submitting.
Employers sometimes try to keep you longer than your notice period. They can't. The notice clause in your contract sets the maximum (and the minimum). If your employer says you have to stay an extra two weeks because they're short-staffed or you 'owe them' for training, that's a request, not a requirement. You can say no. If they then withhold pay or a reference, that's a separate issue and may need ACAS involvement.
Employers can change what happens during the notice period. They can put you on garden leave (paid to stay home) if your contract has a garden leave clause. They can offer PILON to end your employment immediately (and pay you for the unworked portion) if their contract has a PILON clause or if you agree. None of these changes the end date; PILON just brings it forward to the day the payment is made.
The practical advice: resign in writing, state the last working day clearly, keep a copy, and assume the email or letter is the moment your notice starts. If the conversation afterwards becomes difficult, the written record is what matters. ACAS has free guidance on resignation if you need to escalate or take advice on a specific situation.
General information about UK employment law. For your specific situation, contact ACAS or an employment-law solicitor.