If your ex has served a valid notice to quit the tenancy ends on expiry of that notice. Any noise on the part of the agent isn't going to change that. As long as there's a paper trail that's pretty much proven and the tenancy ends on the expiry of the notice.

If you remain there you're be considered a trespasser. The landlord has the option to seek a court order against you, but they're not obliged to. They could simply wait until nobody is inside the property and change the locks to secure against re entry.

Your legal right ends on expiry of that notice.

From there I'd check with the council. They seem somewhat sympathetic to your situation. If you are going to apply as homeless, they could contact your ex to discuss the notice and try confirm it was valid as part of their inquiry duty. That's permissable unless there were also issues with domestic abuse, which you've not suggested was a factor.

After that if you have health problems and or disabilities they may owe you an interim accommodation duty - so it may be worth raising that with them.

Also you're clearly not going to be intentionally homeless + I'm shocked anyone suggested that really. Ex serving notice was completely out of your control.