Possible Clues:

• Popular food fish
• Perhaps Henry the First, although more than a little fishy
• 'Henry 1, although that's fishy and that's flat (7)'
• What gives heart to poorly built swimmer
• Prince only eats one fish
• Friday favourite?
• Seems like Henry I, although it's more than a little bit fishy
• Fish having a party in little house
• Prince's current objection regarding fish
• How 27 across follows 9 across, in short, and that's flat