The main priority of Britain is to hurt Germany. This can be economically, of militarily. Usually the former is easier than the latter. But, if Britain can mount a successful military attack on the Western front, then Germany is in grave danger.
There are several factors that inhibit this, however. The Luftwaffe, time, and to a lesser extent, resources. These are the following steps you must take to ensure a successful British attack:
Step one: The Origin of Attack
Your origin of attack must be safe from the Luftwaffe above all else. This doesn't neccessarily mean out of range, just safe. This may require some help from your American allies. I recommend using the East Canada Sea Zone. Russia can help by sending its "navy" to help protect the sea zone. The British SZ can't be defended anyway. This way, Germany has to divert planes from Britain, and Germany can't risk leaving that navy intact.
Step two: Secure and mass forces
Britain builds an I.C. in E. Canada. America can build an aircraft carrier and a fighter turn one. Britain then builds its ground units in E. Canada, and its air units in Britain. The American carrier with two fighters then moves to protect the SZ. Britain builds 3 transports next turn. Remember, a good attack needs close air support wherever possible.
Step Three: Surprise, surprise!
The transports in E. Canada SZ open a wide array of targets to the Allies. You have your choice between Finland/Norway, E. Europe, W. Europe, and Berlin. The main two targets, of course, are Western Europe, and Berlin. Have a shot at Berlin? Take it. If not, go for a smaller target. Whatever you take is a benefit. Think in the long term.
Step Four: Reinforce
Whatever you take, your allies both have a chance to reinforce
before Germany can do a thing about it. Make sure they can't next turn,
either.