Since it is not a connection but is 2 separate bookings, then BA policy is not to check the luggage through to the onward flight, so they are correct in telling you that you need to collect your luggage

After clearing immigration and collecting your luggage then you will arrive into the T5 arrivals area , so can use the arrivals lounge without issue

You will then need to take your bags to T1 to checkin for the flight to KEF

Dave