Being familiar with neither El Al nor LHR, what follows is entirely in the category of "educated guesses".
There are two broad ranges where noise levels can be affected by operations, those being on approach and on departure. The things that tend to make aircraft noisy on approach would be configuring early and flying down final with lots of drag (i.e. full flaps) and lots of power (i.e. lots of engine noise). On departure, using maximum thrust instead of a reduced thrust takeoff tends to be more noise close-in to the airport, but it results in a steeper climbout, which makes for less noise farther away.
Would "standard operating procedures" for a "high risk" airline tend to require either of these? Hard to say. As far as survivability, configuring early means that if you take a missile close in, you're already in a landing configuration, so losing a hydraulic system or two doesn't affect your ability to get configured for landing. On the other hand, being at full flaps makes performance on a go-around worse if you take the missile and can't change configuration (but need to go around rather than land). Plus, engines running at the higher power setting would tend to be more of a target for an IR (heat-seeking) missile. If you thought you were coming in to a high-threat airfield, you'd probably want a steep approach, meaning lots of drag but a LOW power setting. I have a hard time envisioning a 747 doing this coming into LHR, but maybe they do, spooling the power WAY up to arrest the steep descent at some point close-in. Maybe.
On departure, the max-thrust takeoff DOES get you out of some threat envelopes more quickly than the reduced thrust takeoff, so that's fairly believable. Get as high as you can before you depart the airport perimeter (which is presumably more secure than the areas outside the airport fence). If "always fly a max thrust takeoff" is part of the El Al S.O.P., then it wouldn't be surprising that this would result in higher noise levels close in.
Still in the "educated guess" category, I would wonder if some element of the noise ratings may have to do with how they're calculated. If the rating for British Airways averages out the 747's departing at heavy weights to destinations far away (four engines at very high power settings putting out lots of noise) with smaller, lighter airplanes departing to closer destinations (two engines at reduced thrust, putting out less noise), then their average would be lower than a carrier which is always flying heavy 4-engine jets to a fairly distant destination. Not that El Al would be the only airline in this situation, I'd suspect, but not having smaller & less noisy aircraft to reduce the average may be at least one factor in the ratings.
Without seeing the actual ratings and at least some of the methodology as to how they're calculated (near/far, approach/departure/both, weighted by time of day, whatever else), it's very hard to know what's really going on there. Plus, taking a look at the procedures into LHR & seeing if there is any difference in how El Al flies them and how "everybody else" does. A lot of questions there in order to get a true high-quality answer to what's really driving those results.