My two favourite restaurants in that area are:
Blue Print Cafe
http://www.blueprintcafe.co.uk/and
Tentazioni
Tentazioni Restaurant, 2Mill Street - SE1 2BD - LondonMight be too pricey for what you're after - ie not significantly cheaper than Oxo. I've heard the new restaurant in the Royal Festival Hall is very good, but might also be too expensive.
You could also try Roast (again, not cheap) or Brindisa in Borough Market, though Brindisa is more of a tapas bar than a restaurant and might not be the kind of thing you're after - the food is excellent though.
Roast Restaurant London, Deliciously BritishBrindisa Tapas KitchensA bit further along the river, round the back of Tate Modern is the Blue Fin Building (where I work!) which has several decent chain food outlets in the ground floor - Leon would be lovely for a modestly priced evening meal.
Leon Restaurants - Autumn LeonThere's also Tortilla, which is my current favourite lunch option, but might be a touch too informal for an evening meal.
Tortilla - Home of the Best Tacos and Burritos in LondonTalking of Tate Modern, the restaurant on the top floor is also supposed to be very good, though I've never eaten there - and it has views to rival the Oxo tower.
Tate Modern | Eating & Drinking - Tate Modern RestaurantThe restaurant in the Globe Theatre was OK when I went there a few years ago, but it's more geared up to pre- and post-theatre dining.
I actually rather like Nando's myself. Along that stretch of the river, there's also Pizza Express and the Real Greek Souvlaki bar, which are all fine for chains.
d.