Please clarify...

[NymphadoraBonks]

... how many people from the same household can exercise outside together?

My friend insists it’s no more than two.

No limit on members of the same household, your friend is wrong

She says it’s unclear because more than two people even from the same house counts as a gathering and gatherings of over 2 aren’t allowed.

It’s two. Otherwise everyone group would claim to be related... You always have to cater to the lowest common denominator, and there are literally countless idiots about who delight in circumnavigating the system.
Pointless arseholes.

It’s not two. If you’re from the same household, there can be more than two. See the attached from Gov.uk.

It would be ridiculous if it were two. I’d have to take my three children outside for a walk one per day!

What does a lone parent of four children do?

Pretty sure whole households can exercise together.
The gathering of no more than 2 people applies to meetings etc of people not in the same household. It doesn't refer to exercise because you either to that yourself or iwth people from your household.
I am not sure what those gatherings might be but maybe work meetings that are still going ahead, interviews, etc

X post.

Question answered - TY @Clettercletterthatsbetter

You can go out together in larger groups than two if you belong to the same household and it’s for exercise.

That’s not classed as a gathering.

Your friend is wrong. You can do "one form of exercise a day, for example a run, walk, or cycle - alone or with members of your household" (emphasis mine).

Imagine, for example, a single parent of two young children - it would clearly not be workable of only two of them could go out at once.