Could Britain simply block the Baltic exits?

Would it have been easy for Britain to block a fleet coming out of the Baltic?

Geographically possible, but not easy: Britain first had to neutralize the Danish fleet and might then need a very large force to contain the combined league.

Britain could try to close the Baltic exits, but it first needed a secure base and control of the waters around Denmark. Copenhagen already based the Danish fleet at the approaches a British blockade would have to use. If the League of Armed Neutrality assembled anything near its projected strength, Britain would need a force comparable to the fleet blockading France. A narrow maritime choke point does not make containment cheap when a hostile navy controls the local base and reinforcements may arrive from within.