It's not whether BA will allow it, it's whether the BAA security people will allow it. At LGW sometimes they do, sometimes they don't - makes it very hard for us to be consistent.
As for long umbrellas - they're a no-no if they have any kind of point as they're considered a dangerous weapon!! The BAA people will send you back to the desk where we'll tag it and send it to the outsize baggage belt (they get stuck or lost in ours at LGW otherwise). If you've already checked in your baggage allowance technically we should charge you, but most of us will override an umbrella.