The active ingredient is exactly the same - micronised progesterone.
It is just like buying nurofen vs Tesco's ibuprofen. Both do exactly the same job.
Whilst there are a minority of users who will react to the excipients in one form or the other, and in this case a branded product is warranted, with the vast majority of people it is psychological, and expecting the NHS to provide brand name medication when there is a much more cost effective option is unreasonable.
I am not just talking about progesterone, this happens across all drugs, people want the brand name.
There are very few instances where this is clinically important eg some anti-epileptics.
Also, I would recommend always having your medications prescribed generically, because in the event of shortages you can much more easily be supplied with an alternative by the pharmacy.
If you are prescribed the brand name exclusively and it can't be supplied, this can lead to either going without or a delay whilst this gets sorted out.