I certainly do not think there is going to be any invasion of Iran. Iraq has already turned out to be a lesson in stupidity. It would not make sense to go charging into Iraq whilst the problems in Iraq are still ongoing and there is no easy escape. The military effort for an invasion would have to be far greater than that used in Iraq. Iran is far larger and does not have a similar littoral as Iraq. Any expeditionary operation would be one of great difficulty.
I think if anything is going to happen in the short- of medium-term it will be airstrikes. Though they are not that effective. In any case, thought the British might be and probably will be stupid enough to support the Americans if anything goes on in Iran the British Army and Navy won't be able to lend much of a hand. Poor old Britain is a stretched to its limits.