So, you don't have to be a 'native born' citizen, you can be a naturalized one.
Who can stand as an MP?
- a British citizen
- a citizen of the Republic of Ireland
- a citizen of a commonwealth country who does not require leave to enter or remain in the UK, or has indefinite leave to remain in the UK
And apparently you can be a felon, but not a bankrupt:
Certain groups of people are not allowed to stand, these include:
- members of the police forces
- members of the armed forces
- civil servants and judges
- people who are subject of a bankruptcy restrictions order in England or Wales or a debt relief restrictions order
- people who have been adjudged bankrupt in Northern Ireland
- people who have had their estate sequestrated in Scotland
I don't think that the people who devised the requirements (both US and UK) thought to put in something about not being a convicted criminal/felon. None of them ever thought the need would arise. Obviously it has here. Hopefully it never will there.