You need to obtain an Accelerated Possession Order from the court and possibly even then a Warrant of Execution for bailiffs to physically remove the tenants from the property.
You are fully entitled to receive rent whilst they still occupy the property. I have just been through a similar case and the judge never made any issue regarding rent payments.
The S21 is not dependent on none payment of rent, it is a no fault eviction. This would only become an issue if you were seeking possession via an S8 with grounds of non payment of rent.
Unfortunately you will not be able to evict them legally any other way or any sooner than the court process takes.
You can say whatever you want in your communications, I would suggest you definitely advise the tenants you will be seeking a possession order and, if necessary, a Warrant at a cost to them, if they choose to ignore the S21 move out date.
You do not need professional advice unless you really want to pay out further and hope to recover costs from the tenants. The court clerks will give you all the information you require to submit the application for a Possession Order and Bailiff eviction. See an earlier post on this topic wherein I wrote a detailed list of the documents, costs etc.
I made an error in that I submitted the forms in my name only but our properties are in joint names, the judge sent them back requesting we amend the documents when he noticed the landlord details on the TA, so it does not mean your documents will be automatically rejected.
Being overseas I even had to send a digital copy of the revised form and my signature which was accepted by the court.The court clerks are very helpful and would no doubt help check your application form and documents if you asked at their office.
We have since received the Possession Order and are now undergoing the Warrant application.
I would suggest you have a bit more confidence in yourself especially since you say you have an interest in the law and presumably have done your research into the procedure. I have saved a fortune in legal / professional expenses by conducting all my own disputes and the situation noted above was the first time I was slightly out of line with anything, perhaps I’m going senile in my old age, also slightly out of touch and rushed to prepare the documents before I left UK.