I would have few concerns in central London. There are plenty of police around, and before pubs close at 11pm, there is unlikely to be any potential for problems on the streets/underground.
London is one of the safest cities in the world in my experience.
Having said that, you should of course exercise the usual cautions as in any big city; do not wear expensive jewellery, be aware of handbags and keep wallets away from pickpockets. Keep away from rowdy individuals should you encounter them on the tube (underground).
You should have no problems at all! Have a great stay in London!