Central London is fairly well protected by the Thames barrier, so if you are only staying in central London you will be fine. The only thing that might be disrupted are the airports. If you are arriving in Heathrow Airport then make sure you check before you fly because the parts of the Thames that is badly flooding is all around Heathrow. At the moment it is still clear of danger, but that could change with tonight's expected bad weather again.

I also haven't heard of any issues with the Londin Underground. In past really bad weather some tube stations have flooded, but I don't think any have yet. You should be fine.

Just don't plan a river cruise!

I would also expect the London Eye to be shut due to strong winds (70+ MPH).