Hi I don't think they're quite the same... close to London means the train is quite near to the city ....but closer to London is relative and means the train is closer than it was the last time you asked...you could be closer but still be 500 miles away!

Both are grammatically correct, but - if you think about it - only the first one is appropriate for the situation. 1) Are we getting close to London? This is a normal question to ask. It means "Are we near London now?" 2) Are we getting closer to London? Taking the meaning literally, this would be a strange question to ask - because the answer is evidently 'Yes'. If the train is travelling in a south-easterly direction from Manchester to London, every inch that you travel is obviously taking you closer to London.

Both OK in my opinion.

Both are OK. they are the same meaning.