A2B, holding perfect altitude in the circuit is only needed when other traffic is around, and holding the perfect approach speed is only needed when flying into seriously short strips.
All other occasions, it's very well possible to fly a full circuit with zero instruments. Yes, you will not fly at the perfect 1000 feet and will not have the shortest landing roll possible, but you will have gained valuable experience in controlling the aircraft when things go pear-shaped. That's what's learning to fly is about, for a significant part.
Of course if you have a for-real pitot/static failure you're not going to fly into a situation where altitude holding is critical, or into a seriously short strip anyway.