Lots of options in the area. The easiest to get into will be at the swan and dolphin. In December I ate at both Il Mulino and Bluezoo. Both were great, bluezoo was outstanding.
In the area I also recommend flying fish, trattoria al forno, ale and compass and yachtsmen steakhouse. All are walking distance.
I do not recommend Big River Grill. That was awful in December.