Minimum Connecting Time
Airlines at airports worldwide publish Minimum Connecting Times (MCT). The reservations systems are programmed to respect such times. The system I have most experience with is Galileo and it will not offer a connection that is less than the MCT. If someone deliberately books the so called connecting flights separately (but in the same booking) the system will permit this but warn the user. I believe the other systems do the same thing.
Therefore, in principle, the airline and airport believe you will make your connection but that rather assumes everything goes well. It also assumes that any bags are through checked.
So, back to your original question do BA and DL "interlink"? It's actually called "interlining" and, last time I looked, BA and DL do interline. The fact that you have one ticket covering both flights supports that because baggage and ticket interlining are usually covered in the same agreement.
So, when you check in at Glasgow point out to the agent that you are continuing to New York and ask them to through check your bags. On the resulting bag tag you will see the codes LHR and JFK. If you only see LHR the bag has NOT been through checked.
Through checking the bag does NOT mean you will automatically get boarding passes for all flights. You will probably have to visit the connections centre at Heathrow to do that. The LHR website explains how that works.
One last thing. It is possible that when you booked the flights the MCT applied. I have seen (rarely) situations arise where the MCT is revised between booking and travel. I have also seen flights rescheduled. Either change could result in a connection which was valid to become invalid. Try booking the flights on an online website such as Opodo and you can probably check that out yourself. Otherwise call the people you booked it through and have them verify that the MCT is still valid and if you don't get satisfaction from them you could try phoning Delta.