This is getting tiresome
UK AIP ENR 1.6.4 has the answer.
(a) Tip to Operators: Adressing your flight plan to EGWDZQZX will help a lot. (IFPS will not do this for you)
(b) Tip to Civil sectors: Don't ask the Mil if they 'want to work it', just tell them that you have traffic for them, as pointed out by norvenmunky
Tip (a) combined with tip (b) has an estimated 99%(1) success rate. For the other 1% of occassions, the ICF is 135.15, just call and hope it isn't that Wing CO at Swannick Mil with the official line that happens to answer the call (yeah, right!)
Happy aviating peeps.
(1)82% of statistics are made up on the spot.