If the obstacle is on the recognised trails (whatever grade), I will leave it alone unless it is an easily removed fallen branch. In my experience, the Forest England team will clear the obstacle quickly. Unless it is the aftermath of a big storm, in which case it may take a week or more. I will still leave them to it.
But if I am off-piste, I have a different approach. The Forest England staff have enough to do without also maintaining the mass of trails all over the forest, even if it is under their control. They have neither the budget nor the staff to monitor the extensive network of trails that cover the forest.
If I can, I will remove any obstacle I find. It might take a few visits, or even require assistance. If the tree is up to 7" diameter, I will saw through it with my folding saw and drag it out of the way. Above that I leave it alone and find a way around it. The obstacle can be trees or branches that have fallen across the trail. Sometimes they are branches that have snapped and are hanging above the trail low enough to impede passage. I do the same with brambles, nettles and bracken where they provide an obstacle to passage or just a safety hazard. Brambles can be released by winds and can appear apparently overnight, blocking the trail. I have not forgotten leading a group ride down a steep slope that I had checked the day before and ended up with a thumb-thick bramble in my mouth. I had trapped it with my teeth, but if the guy behind me had ridden into me I would be the owner of a wider smile than currently.
I am very aware of the hazard of stored energy in a fallen tree. I always survey the fallen tree to see if it might be under pressure from another tree, or appears to be bent. Because I am sawing by hand, if there is stored energy, the tree may start to bend and/or make creaking sounds as I cut through it. I adapt my approach appropriately. I always ensure that my feet and head are well out of the way. Trees may spring in any direction including upwards! They can just drop, or even roll down any slope. Be careful and use your head!

In the forest no-one will hear you scream!
