I suspect they would try more of a German style lockdown first rather than go straight to a France style -- in most countries, they are gradually increasing the restrictions and seeing how people react.
Here in Germany this is what lockdown means:
All non-essential shops are closed. Essential shops include all food shops, pharmacies, bike repair, newstands, laundromats. Food markets can stay open but not other kinds of markets.
Cafes and restaurants were allowed to stay open during the day but now they are also closed. They can do takeaway but cannot allow big queues or gatherings.
Amazon and the post can still deliver.
All non-essential workers are supposed to stay home. The list of essential workers is rather limited.
You can go out alone or with your immediate family members in order to: buy food or medicine, go to the doctor, visit elderly family or pick up your child from the other parent's house, help vulnerable neighbours, exercise, a few other things.
Parks and pools are closed. They would never allow the scenes from the weekend here.
The rules are very clear and people are actually following them well, that's why we don't have a nationwide total lockdown yet.
I don't know how they would enforce all this in the UK though without legally requiring people to carry ID.