The move would require an act of Parliament, which would have to be approved by MPs and peers and would come into effect when given royal asset by the King.
It would also need to be supported by the 14 Commonwealth countries where Charles III is head of state, including Canada, Australia, Jamaica and New Zealand.
The last time the line of succession was changed by an act of Parliament was in 2013, when the Succession to the Crown Act restored individuals who had previously been excluded because they had married a Catholic.
The last time someone was removed from the line of succession by an act of Parliament was in 1936, when the former Edward VIII and his descendants were removed due to his abdication.
Liberal Democrat leader Sir Ed Davey said police should be “allowed to get on with their job, acting without fear or favour”.
He added: “But clearly this is an issue that Parliament is going to have to consider when the time is right, naturally the monarchy will want to make sure he can never become King.”
The SNP would support removing Andrew from the line of succession if legislation is required, according to the party’s Westminster leader Stephen Flynn.