Well, it's going to depend on
1) how busy we are
2) how busy the next sector is
3) whether Lille/Paris/Brussels decide to call us
4) the level you have filed at
5) if Europe have had a yes on the call before (if not they may call London Info who will almost certainly give a service where London control may not)
6) the day of the week
7) the time of day
8) other sector factors such as para dropping
Outbound is more straightforward as you are largely with the flow of traffic, so your being (I'm assuming, sorry) low and slow is not so much of an issue.
Coming back in, not so simple. You are likely to be mixing it with all the Thames traffic hence will often get descent and handed off to Thames. The airspace around there can be a bit complicated!
In general in the LTMA we will try and give you a service if we can, but don't underestimate how complicated you can make our sectors. We try, but we are balancing all the time now and so sometimes it will be no. Nothing personal.
As an aside, London information are not allowed to talk to aircraft in controlled airspace so if we can't give you a service they will have to ask you to ensure you remain outside.
Ask more if there is anything I haven't covered or you'd like more info.
Cheers,
Northerner