Should I worry about rain getting inside my frame? I commute to work every day and lock my bike on the street. 

I have a nice saddle so I remove my seat post and take it into work with me. 

This obviously leaves a hole open to the inside of the aluminium frame. Living in London it often rains. Should I worry about raining getting into the frame by this hole and doing damage? And if so what should I cover the hole with?
It depends on the frame material what effect the water inside the frame will have. A lot of frames have a small hole drilled at the bottom of the bottom bracket casing. If there is no hole there you can drill one yourself. I have done this on aluminium frames before and it is very easy. Use a 4mm drill bit and drill through till you cut into the bottom bracket void. There will be a gap internally between the frame casing and the actual bottom bracket. A hole this small in the centre of the bottom bracket casing will not affect the strength of the frame but will allow water to drain. I have found frames fill up with water even with the seat post in place if ridden in the wet, so putting a cork in the seat post hole probably won't make much difference.