Although the American and British democratic systems are very similar in many ways, there are differences that are rather significant. For one thing, America has a written Constitution, whereas the UK does not. The American President is elected directly, whereas the British Prime Minister is normally the leader of the political party currently elected to form the government, though this has not always been the case.
In 19 states, there is a Recall facility, which provides for the removal of an elected official under certain conditions. Where a recall petition is generated without cause, however, there is a risk that the recall be deemed “frivolous” if successful. Note that the Recall facility does not apply to Federal officials.
Article 5 of the constitution provides for changes to the American constitution, as follows:-
“Altering the Constitution consists of proposing an amendment or amendments and subsequent ratification.
Amendments may be adopted and sent to the states for ratification by either:
Two-thirds (supermajority) of both the Senate and the House of Representatives of the United States Congress;
By a national convention assembled at the request of the legislatures of at least two-thirds (at present 34) of the states.
To become part of the Constitution, an amendment must be ratified by either (as determined by Congress):
The legislatures of three-fourths (at present 38) of the states;
State ratifying conventions in three-fourths (at present 38) of the states.” (Wikipedia)
It is precisely this mechanism that is being used in the push to apply Term Limits to all American politicians, and not just the President. This is necessary, as their system is overloaded with career politicians who need to be replaced.
The process has already been started, and you can monitor its progress by regular visits to Term Limits for Congress
The UK has the same problem with career politicians, but there is no convenient mechanism to deal with it. We have to rely on the tried and trusted system of the “Petition”.