You could just stay in the baggage area if your flights are quite close together.

One of the Costas is just outside the baggage reclaim area you really can't miss it. If you are arriving first though you could get a Costa upstairs then take a seat that looks over the luggage area. From the vantage point you can see everyone exiting the baggage reclaim area. Walk through arrivals and you will see and escaltor which takes you to the upstairs costa.