c. london sunday early AM parking and breakfast

[ADP68]

I'm thinking of organising a Central London Sunday eraly-morning drive for the Rolls-Royce club in Summer and hope we can terminate in a square with parking, close to a cafe where we can get a fry-up. Someone has suggested Wilton Square, but I don't think there's a fry up joint that close. The alternative is Dorset Sq as there's a cafe opposite Marylebone. Does anyone have any ideas? St James' Sq? it would be good if the parking were free or at the very least, not resident's only. And the cafe needs to be open at about 0730-0800ish. It doesn't have to be a square either, just a road with good parking
Thanks
Andy