Rab can confirm, but the Reduced Longitudinal separation trial has been delayed and it's still a basic 10 minutes on all tracks for now.
The Shanwick boys and girls also operate, as stated, on a first come first served basis. That means that if you request FL340 with a MAX of FL360, and no one else has already taken FL340, you get it. They won't give you a higher level just on the off chance that someone else might come along who can only take 340. It really is that simple. If you don't really want to go to 360, then don't give it as your MAX. Your options then, if 340 is already taken, will be a track change or a lower level. On a busy day, the level could be down at 280 if everyone else has got in ahead of you and grabbed all the other levels. Shanwick do have stats on the number of aircraft getting their requested level and entry point. I believe the % getting it is in the 90's. Maybe Rab can confirm ?
The point about Chinese and Middle East aircraft is that there will potentially be more competition for prime levels. These aircraft will already be up at those levels and can make very early clearance requests with Shanwick, often before a UK departing aircraft has even left the ground. The further away you depart from the Oceanic boundary, the earlier you can get in with your request. Increasingly, you might start to find there are fewer economical levels left when you have departed Heathrow, negotiated the London TMA, and then settled your cockpit workload down enough to put in the Oceanic request.
Ultimately you have to ask ATC for what you really want, but if that's not available, then you need to consider what is your least worst next option and give ATC the information to allow them the chance to provide it.