To realise what London info can provide it's probably best to understand exactly what they are not and what they are.
It is not loads of people sat round radar screens who can tell you where everyone is. It is not a service which will separate you from everyone who may be near you when you're not in LARS coverage.
London info consists of 2 or 3 staff sat at a desk with a large map of the UK in front of them. Whenever you call they will write down your details on a paper flight strip and put it in front of them with all the rest of the people who call. They will endeavour to give you any information on a flight that is blatantly close to you but that is not their prime job.
Services provided - mainly the following:
Alerting service
If you're flying over a desolate area of the UK (Welsh mountains, English Channel, Irish Sea) where there is no ATC to provide this service then you can scream help and they will give you what they can - having your details will enable them to better inform D&D and any other interested parties. Needless to say every Tom, Dick and Harry who calls them on a summers day when he's tootling around the SE of England and just wants someone to talk to seriously degrades this service.
Flight Information Service
Information pertinent to the safe conduct of flight - danger area activity info, weather information, airfield availability, pressure settings and the like.
Airways joining clearances
Obtaining airways clearances for aircraft operating outsde Controlled Airspace who wish to join the airways system. Coupled with this is the acceptance of airborne flight plans and the activating of flight plans if you haven't managed to do it via an ATC unit.
There are a couple of PPRuNers who work there who can fill in the gaps - but the above are the main reasons for its existance.