The airport does "open" one Saturday afternoon a year & this is for the annual LCY Funday which I believe is the only time single engine aircraft are permitted to use London City Airport (I know they've had a Spitfire in during this event before) but all aircraft are invited & I think LCY ATC iS downgraded.
7th July I believe this year. A great event. Well worth a visit. Free to get in but they do expect you to spend some money which all goes to the local childrens hospice 'Richard House' which looks after terminally ill children. The flying display is awesome but it's a great community event. I will be trying to get there for about the 10th time in a row!