I do realise that this answer, being months after the OP, will be too late for the original poster. I just post this as information for anyone browsing the forum.
However, it is possible to travel moderately independently in Iran even as a UK, USA, or Canadian passport holder.
I believe that how it's done is this. You have to have a licenced tour guide with you, and for your travel plans to be approved. So, you can't really just go there and go wherever you want. However, it is possible to make up your own plan, and then give it to a tour agency for them to make it a reality and supply the guide. If there were, e.g., three people travelling together then you only need one guide, and sharing the cost of a guide between you will mean that it isn't too expensive. in fact, if you get a driver-guide, then that covers your internal transportation as well. However, internal transport in Iran can be very cheap in any case.
For larger groups, I would imagine that it's possible to hire a larger vehicle. I believe that one guide can guide quite a few people, spreading the costs further. It's also, I'm told, possible to hire non-driving guides who will go on public transport with you.
As far as I understand it, what you won't be able to do is suddenly change plans. You'll have to follow the travel plan you submitted. But, you can go wherever you want whenever you want, provided that you decided this before the trip.
(I went on my New Zealand passport and hence didn't have to do this myself.)