We're seeing more questions from people wanting to apply for a UK visa and have a criminal history of some sort. Some people worry that disclosure from their past may adversely affect their application and so they are reluctant to make a disclosure. Others are just confused about what it has to do with and why visa applications require a person to list convictions.
One of the reasons people find it confusing is that there are about 3 or 4 different facets of immigration law where criminal history is relevant, and there's no place that consolidates all of them into one easy-to-understand framework.
Let's list a few of these facets...
Overall, the Home Office (acting in the persona of Secretary of State for the Home Department, or SSHD) has the power to refuse a visa if he/she thinks that having the person in the UK is not conducive to the public good. SSHD can also, by the way, grant entry to someone with a criminal history if he/she thinks that their EXCLUSION would be invidious. Both of these powers are derived from the 1971 Act.
Next, there are aspects of European law which bear on who and who cannot get a visa. This facet is a lot more confusing because the UK has opted out of various EEA provisions. I have observed that sometimes SSHD will pull an EEA provision out of the hat and use it to their advantage even if the UK has already opted out of the provision.
Next, if the person's conviction has to do with something that requires vetting for employment (like a child worker), it can impact an immigration decision.
Next, the 1971 Act (later enhanced by the 1981 Act) introduced a 'good character' requirement. Some, but not all of the 'good character' requirement touches on criminal history.
Also, the 1971 Act made it a crime to enter the UK without entry clearance if the person has a conviction that resulted (or would have resulted) in a year or more of jail time. The 1998 Act added provisions for material ommissions and 'deception by silence' in immigration applications.
Lastly, as of April 2011 a person cannot successfully apply for settlement with an unspent conviction.
So those are the various facets of the rules that come into play when a person has a criminal history. Taking all of those into account, there are some other things to consider...
The Rehabilition of Offenders Act 1974. This act defines how convictions become 'spent' (i.e., no longer requires disclosure). The act itself never mentions immigration, but three successive governments in the UK have interpretted that the provisions of this act also apply to visa applicants overseas. So if someone wants to use the 1974 Act to avoid disclosure, it's ok to do so. The issue to bear in mind is that foreign legal systems are not comparitve, and this could lead a person to think their conviction was spent when it actually was not.
Another thing to consider is the recent strengthening of Paragraph 320 of the rules, which stipulates a ban for people who have engaged in deception or similar abuse. Also the 1981 Act provides SSHD with the power to revoke a person's ILR or even citizenship if he/she learns that an immigration decision was made with false representations.
Another consideration comes in the form of Article 8 of the European Convention on Human Rights. This can be used by a court to force SSHD to issue a visa regardless of his/her objections.
Lastly, there is a body of case law (where people have been to court over this question) and previous readings from the Policy Unit on how some of these various facets should be interpretted. These can also be consulted to see if there's anything relevant to an individual's circumstances.