Shouldnt be too bad, but, early evenings does get clogged up within a mile of Broad Street on the inner ring road, though it isnt central London , so traffic does move, albeit slowly. Be aware of the congestion/air tax.
If going to the O2, we park up around 5 mins walk from there on a side street, anywhere around Upper Gough St. The Keg and Grill there does a great curry, as well as being a nice enough pub, albeit limited in its beers, the Craven Arms just up the road has a good selection of beers in.
Parking round there is free on single yellows after 6.30pm iirc. There are very few signs that tell you that, as it is a parking machine area, so they want you to use the paid for parking spaces.