Is school being unreasonable about the park?

Bonkers.
It is informal childcare surely?

That's crazy. Even if you did take him home with you, you are allowed to have people in your home to provide childcare to allow a parent to work, which is exactly what you are doing.

I’m amazed that you have DC at a school where the staff have time to monitor this nothing situation.

And YA obviously NBU whatsoever

In all my years of school (DS in yr 6) I have never had cause to speak to the head teacher. On this occasion, I would. I think wires are crossed somewhere and they need uncrossing.

I would tell them you are each others childcare bubble and its therefore within the rules

That's crazy, you're allowed an informal childcare bubble for this purpose. Or school will let them leave independently from year 3 if the parents want them to as well.

Totally ridiculous!

That's informal childcare and you could take the child to your house if you wanted. Not for the school to police, especially when they're policing it wrong!

There aren’t any lockdown rules atm as we aren’t in lockdown.

YANBU, they are definitely BU.

It's childcare. And safer with Covid to play outside than to go back to your house anyway.

Support bubble is totally allowed. Not their job to police it. Friends mum should give them a telling off

Aside from anything else, I would be objecting strongly to the school declaring me a liar in such a way. Totally out of order.

This doesn't make any sense. Surely you would be allowed to take him to your house regardless as it is childcare? I might be wrong on that one but I don't think so. Even if you were breaking rules, which you are not, I don't think it is their right to refuse to release the child to you if it is the parents wishes and you are a named pick up person. They aren't the police. So so strange and unreasonable of them.

If ask to discuss with as senior person as you can manage. Clarify that you are not in breech of the rules and ask them to confirm in writing that they will be be preventing you from collecting the boys.

Disgusting behaviour from the school. Definitely speak to the headmaster and whoever is above the headmaster if they're no use.
You're allowed to provide childcare so they're wrong in the first place.
But they also have no right to refuse to hand your child over when the mother has told them to give him to you. I'd have thought that's a serious breach of some safeguarding rules, they cant just keep a child back as and when they please unless there's a real concern about the childs safety. What happens when your son starts telling them that he's going to a party at his cousins house this weekend? No you're not having your son back because we think you're going to break covid rules

I would raise it with the head. I have had teaching assistants tell my daughter all kinds of incorrect information about Covid rules in school, and got a bit too enthusiastic about 'enforcing'. When I questioned it with the reception staff they checked and got back to me basically saying 'yup, no idea how she got that from the clear rules circulated by the head' and they had a word and the problem stopped.

Unless school have a policy in their risk assessment to only release children to members of their family or named childcare providers then I don't think they've got a leg to stand on.

I wouldn't get into childcare bubbles with them because if later you need to use grandparents or form a bubble then you technically can't as childcare bubbles are fixed.

Speak to the head about the school's policy for releasing children during covid and take it from there.

Absolutely crazy and even in a tier 3 area childcare is allowed. I would speak to the other parent and both of you contact the head directly. I'd be fuming.

WTAF!! Even if he was coming to your house, informal childcare is allowed. They should get their facts straight and butt out. Give the head a call.

I'm kind of with the school, but not because you were picking the child up. I despair of the overrun playgrounds outside of school where all the 'bubbles' are gone as they all mix together climbing on things and touching things.

defeats the entire purpose of our school bubbles

The school cares about protection of people from Covid 19, that is a good thing. They contacted the other child's parents, a good thing. Wanting confirmation of this arrangement from them, a good thing in my view.

Telling you off, and the other parents, not good and this is what I think you should raise with them.

Rule of 6 outside anyway so this within the rules.

Incidentally, the government not going down to borough level and your area being in tier 2, and the nonsense of Holy Island/rest of north Northumberland, Tunbridge Wells and northern Lancashire being in tier 3, I have sympathy and agree with you is nonsense.