Can I join new workplace even though employer hasn't accepted my resignation?

I have been working at a company for 2 months 2 weeks and have sent in my resignation four days ago via email. According to my contract, I am currently on probation for another 4 months and can be terminated at any time as per the company's will. There is no notice period stated on my contract either. Additionally, this company refused to cut PF despite having over 50 employees in the workplace. Out of courtesy in my resignation letter I also offered a one week's notice to complete any pending work I have. Upon receiving my email HR called me up 2 hours later and verbally accepted the resignation. I applied to a job at a different company and was able to secure the position. I am due to start work there 2 days after the notice period I gave the company. However, the current HR and Manager team have refused to accept my resignation officially by email and have refused to send my relieving letter and salary slip which I require for onboarding at my new job. Once again reiterating- ACCORDING TO MY CONTRACT I AM NOT OBLIGED TO SERVE A NOTICE PERIOD AND I CAN BE TERMINATED BY THE COMPANY AT ANY TIME SINCE I AM IN THE THIRD MONTH OUT OF THE 6 MONTHS PROBATION PERIOD. What should I do in such a situation?