Onlookers who saw them at The Dove in Hackney, east London, told the Daily Mirror newspaper: 'Katy didn't seem to care that they weren't in a fancy, expensive restaurant.
'She was giggly and happy with Rob and some friends, and she even sneakily held his hand under the table.
'She was saying she was excited to be back in London. She was saying how much she loves it here.'
Last night, the pair enjoyed another date after Rob accompanied Katy to ITV studios where she was filming the Graham Norton's talk show.
They left the studios together to go to Wilton's Bar in east London and then to the Market Café in Hackney for some food.
Katy previously told friends that Rob had made her feel 'sexy and alive' again following her split from husband Russell Brand in December after 14 months of marriage.
A source said: 'Rob was the first guy Katy had been with since splitting from Russell.
'She was still extremely fragile but had told pals their two weekends at Coachella together made her feel 'sexy and alive' again.
'Even when Rob left to continue touring America with Florence they would speak on the phone up to three times a day and she'd be constantly texting him.'
Katy's divorce from Russell is set to be finalised in July.