This will be moved, but as I have the info up for you, I can post it here. Remember this doesn't show the load (only Emirates staff have access to this - and you will not get it unless you know someone). What this shows is what prices / seats Emirates would be prepared to sell you if you lived in the UK! But it gives you a good general feel.
PER DXB
21/0540 1240 EK 425
F4 A4 J7 C7 I0 OC P7 Y9 E9 R9 W9 M9 B9 U9 K9 H9 QC LC TC VC GC XC
DXB LHR
21/1605 2000 EK 5
F4 A4 J7 C7 I0 OC PC Y9 E9 R9 W9 M9 B9 U9 K9 H9 QC LC TC VC GC XC
What this tells me is that the flights are busy, but not overly packed in Y & J, and impossible to read in F but somewhere between empty to middling!
I will also add that Emirates are the only airline i've been on that has shown something similar on the day of departure for me, and then subsequently been oversold by 40 people at check-in. They manage their loads very well!
Y Seats available for pre-booking: PER-DXB = 233, DXB-LHR = 150
I think you've a great chance of getting a row of 3 for 2 of you on PER-DXB and less so on DXB-LHR.
Happy flying, and do report back