No extradition without evidence being tested in UK courts.
No extradition for things that are not offences under UK law.
No extradition for offences that took place in the UK (USA wire transfer, computer, hacking, antiques purchases, etc).
This should apply equally within the EU and outside. Should apply even if a Eurpean Arrest Warrant has been issued.
Extradition should also be subject to a UK Public Interest test and the Home Secretary should have the right (rarely used) to quash it.
Why is this idea important?
Laws, standards and procedures vary.
Some administrations are corrupt at local or national level.
Some prosecutions are politically inspired.
If these laws are not altered controversial UK politicans and their family members WILL be targetted by foreign businesses or people with differing politics.