I'd echo the previous poster, around Trafalgar square is probably your best bet but nowhere really stands out. In reality an 'authentic British place to have a snack' is probably a take-away sandwich/wrap and a coffee from Pret a Manger but suspect this isn't what you mean

The National Gallery Cafe, as mentioned, is quite nice. If it's a good evening weather-wise, The Trafalgar Hotel (on Trafalgar Sq!) has a roof-top bar with good views over that part of London (it's maybe 10 floors up so don't expect Empire State Building heights).