For checking Heathrow slot availability, go to:
https://www.online-coordination.com/...abid=AvailWeek
Then select LHR and enter the date in a DDMMM format (e.g. 09JUN). Green = slots available within the hour. If you then click on the hour, it will show you where exactly the available slot is. You can't book yourself, but Signature can take care of that for you.