© Jessica AllenJessica Allen (left) and Eliza Moore have now learned their lesson
The women were also told the hot drinks they had brought along were not allowed as they were "classed as a picnic".
Guidance for the current lockdown says people can travel for exercise as long as it is in their "local area".
The police force involved, Derbyshire Police, said driving for exercise was "not in the spirit" of lockdown.
One of the would-be walkers, Jessica Allen, assumed "someone had been murdered" when she arrived at Foremark Reservoir on Wednesday afternoon.
"As we drove in there was a police van, a police car, and there were loads of police there," said Ms Allen, who lives in Ashby-de-la-Zouch in Leicestershire.
"I genuinely thought someone had been murdered; the place is normally so quiet. The next thing, my car is surrounded. I got out of my car thinking 'There's no way they're coming to speak to us'. Straight away they start questioning us.
"One of them started reading my rights and I was looking at my friend thinking 'This must be a joke'.
"I said we had come in separate cars, even parked two spaces away and even brought our own drinks with us. He said 'You can't do that as it's classed as a picnic'."
Her friend, Eliza Moore, said she was "stunned at the time" so did not challenge police and gave her details so they could send a fixed penalty notice.
"Just seeing a police officer anyway is quite scary for some people and we were really not expecting to be approached and to be told we were doing something wrong," she said.
"We don't want to get away with it if we have broken the rule, but it seems a bit unfair that you can be fined on something that's so vague."
Comment: Thank goodness for the police. Without them, crime would be running rampant across the land and no one would be safe. We are all safer now knowing that these two criminals are not stalking the wilderness drinking lattés. Onwards into the glorious future! All hail the New Normal Order!