So for Eastern from Teeside there will have to be some through check in facility in place otherwise you will have to collect bags if you have any at the arrival terminal. Transfer with your bags landside. Check in again for your next flight and go through security. Hopefully something will be in place to avoid this.
If there is, nothing has been announced. As far as I am aware, Eastern have no agreements with any other airlines at Heathrow. So, I'm curious as to why the airports press release says:
The machines, fully compliant with Department for Transport regulations, will also make onward connectivity to Amsterdam Schiphol and Heathrow even smoother by removing the requirement to go through their security processes.