Welcome Super Gran. Silver birches give dappled shade and are quite light and airy. I don't think they would block out the light completely.
What sort of soil do you have? Most magnolias like soil a bit acid. I have alkali soil and I planted magnolia Leonard Messel which is very similar to stellata with pale pink flowers and will grow in an alkali soil. But it's a bit strange that you already have a stellata that's OK. They hate drying out in summer (unlikely last year!), they don't like cold winds and spring frosts can damage the flowers.
If you go for birch I would suggest making sure they are one of the very narrow varieties. I have some, but have forgotten the name! Katsura makes a very nice subject as well - there's something elegant about it.
Hi all, been busy so no blogging. Good news my magnolia stellata has burst into life I put new compost around with some grow more pruned out all the dead branches and held my breath! Gradually it started to leaf. It won't win any prizes but it's well on its way to becoming a tree. Thanks for your advice.
Hello Super Gran, good news. Maybe flowers next spring!