The minimum statutory notice an employee must give their employer is one week, but your employment contract can require you to give more notice than this. Check the terms of your contract and any handbook.
If your employer has committed a very serious breach of the employment contract, you may be able to end the contract immediately. Take care. Any tribunal deadlines will start to run from the moment the employment contract ends. Take prompt legal advice if you are planning a tribunal claim.
Your employer does not have to "accept" your resignation or notice, in order for you to bring the contract to an end.