Lo,
First of all, a LARS frequency will generally be better than London Information. London are great when there is no LARS coverage, and also for certain specific situations such as crossing the Channel, but since they don't have any radar they are quite limited in what they can do for you in many cases.
That aside, the answer to your new question is "it depends". How high are you? How close to the airfields? Do they have ATC, or just A/G? How busy are they?
Remember that you can not enter an ATZ without obtaining enough information to do so safely. In practice, what this generally means is that you need permission at a controlled airfield, or radio contact at an uncontrolled airfield.
If you're staying outside the ATZ, then it's more complex. If you're more than about 2500' above airfield elevation, directly above the airfield, then the airfield's traffic will most likely be below you, and there's no need to contact them. If you're 3 miles from the airfield, technically outside their ATZ but on a common entry/exit lane, then it's worth giving them a call - even if you're up at around 2500' above the airfield, since joining and leaving traffic could well be climbing/descending through that height. Basically, if you use a bit of common sense you probably won't go wrong. Local knowledge helps, too, so ask instructors at your school about your own local area, and when you're going outside the area, ask on PPRuNe if in doubt.
FFF
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