I would never say no to a lunch in Blacklock, absolutely fantastic establishment.
I’m going to go a bit rogue and say you can get some of the best burgers in London at the Lord Nelson in Southwark, which would work well with the Tate Modern.
It’s
Very edgy, informal atmosphere, but good food. Also large selection of craft beer.
Lord Nelson
020 7207 2701
https://goo.gl/maps/1ULr2Xwc3D349yKS6
If you get delayed or can’t be bothered to go far from Paddington on the day, the Paddington basin is nice.
There is a good beer selection and interesting food on the Darcy May green barge, if the weather is nice, you can sit on the roof.