I ended up going for plaice fillets (grilled) with a side order of peas, while my companions opted for fried haddock with chips (x2) and the swordfish with tomato salsa. My plaice was perfectly cooked - golden and crispy on the outside and succulent within - and the haddock and swordfish also went down well. Despite this, the meal was still probably a bit (OK, very) expensive for what we actually got - given the simplicity of the preparation and the lack of fancy extras, £20 a head seems a lot for a one-course lunch. Then again, Sweetings does have a great sense of history, and you're paying for the 'old-boy' feel as much as anything else. All in all, I'd say it was worth it for a one-off experience, but probably won't be going back any time soon.
*Although little variety elsewhere: if one of your party doesn't eat fish or seafood, they'll have to stick with side orders of potatoes and peas.