Sure, sow40. Expertflyer can be a little hard to understand in the beginning but you will quickly get the hang of it. Basically you choose "Award and Upgrade Availability" from the left menu then enter your Departure city, Arrival City, Date, Airline (EK is Emirates), and then number of seats (4 in your case) and the fare bucket you need (D Bucket for Y to J upgrades) and it spits out a result saying that for instance (I just picked a random day in the month you mentioned) on May 18th EK 40 Departing at 2:20PM has at least 4 seats in that bucket so you would be good to go. Neither of the other non-stops that day to DXB from BHX have enough availability to upgrade 4 people from Y to J. You do the same in reverse on the date you want to come home, assuming you want to upgrade both ways.

You want to look for the column that says "Seats". It will even show you a current seat map if you want so you can see which seats are available. Quite powerful, expertflyer.

Hope that helps!