They are both quite overgrown and I need to reshape them. Can I cut them back to just above the ground and if so, when should I do it?
The best time to prune the burning bush is in late winter or early spring; for the forsythia, you will want to wait until just after the flowering has finished.
You can cut both shrubs back very hard, that is to just above the ground, choosing to live with a somewhat stubby look until they grow up again, then in future years, just prune to remove dead or crossing branches and for shape.
However, in the case of the forsythia, that approach will promote a great deal of rapid, soft growth and soon the shrub will be untidy again. It would be better to cut 1/4 to 1/3 of the oldest canes right to the ground each year for a few years. Note that you want to avoid having the long canes bend down and rest on the ground, since they tend to take root and further complicate the shape and mass of the shrub.
Just remember, the forsythia’s normal size is about 7 feet tall and 10 feet wide.
For more advice about growing forsythias, see our reply to an earlier question here: forsythia pruning.
And for an excellent guide to growing shrubs, we have posted a Gardening Guide, Ornamental Shrubs for Various Light Conditions, which you can see here.