Don't think they can check through from LGW-AMS-LHR-DXB, BA won't check through LHR-AMS-LHR-DXB for example on separate tickets.

Unless you can leave your bags at LHR or go HBO, then just ask at LGW checkin and show your onward ticket from AMS and if they won't through check then you will need to collect at AMS at recheck.