What is the 'spent-leave', and how does it work?

Also called the "6 out of 12 rule".  To begin, let's have a look at the IDIs...

"...There is no restriction on the number of visits a person may make to the United Kingdom nor any requirement that a specified time must elapse between successive visits. The fact that a person has made a series of visits with only brief intervals between them would not, in the absence of any other relevant factors, constitute sufficient ground for refusal.

It is reasonable, however, for the immigration officer to consider the stated purpose of the visit in the light of the length of time that has elapsed since previous visits. A visitor should not, for example, normally spend more than 6 out of any 12 months in this country (but see Section 3 of this chapter in the case of visitors for private medical treatment)..."

Commentary: The so-called 'spent-leave' rule is not mentioned in the official UK immigration rules, but rather it is a constructive rule that can be used by an Immigration Officer in determining whether or not to allow a visitor to enter the UK.

The rule states that a visitor should normally spend a maximum of six months out of any twelve months in the UK; and attempting to stay for a longer period is a signal that the applicant is not a genuine visitor.  Also there is a justifiable perception that a person who visits the UK frequently and stays for a long time is using the visitor programme as a prelude to settlement.

A court decision on this rule is found in "Oppong (visitor – length of stay) Ghana [2011] UKUT 00431 (IAC)" stated...

An application for a visit visa which, if granted, could result in permission to spend more than 6 of 12 months in the United Kingdom is likely to be scrutinised rigorously but it is wrong to refuse someone entry clearance as a general visitor just because they have spent more than six of the last twelve months in the United Kingdom. In certain circumstances a person can utilise paragraph 41 in order to visit the United Kingdom to provide temporary care for a person present here.

 In this case, the court established that caring for a relative is a tenable argument against refusals based upon the spent leave rule.

I entered the UK in July and it is now January. Does my six months automatically renew because it is a new calendar year?

No. Calendar years have nothing to do with it. It is a rolling year which begins on the date you last left the UK.

I entered the UK in July, then in December I went to France. When I returned to the UK, the IO stamped my passport with a visitor visa expiring in June, and this will make more than six months in a twelve month period. Am I in breach?

No. If your current visa has not expired, then you are not in breach. The 'spent-leave rule' only works upon admission or application, and if you were "stamped in" for another six months, then you may stay without violating the 'spent-leave rule'. 

Update 18 May 2012

In a recent case heard by the Upper Tribunal entitled "Sawmynaden (Family visitors – considerations) [2012] UKUT 00161(IAC)", the appellant applied for a family visit visa and was refused.  The ECO provided this rationale...
 

[...] With your proposed trip, you are intending to spend a further six months in the UK (which would make a total of 14 ½ out of the last 18 months in the UK). Whilst there is no restriction on the number of visits a person may make to the UK, nor any requirement that a specified time must elapse between successive visits, it is reasonable, however, for the ECO to consider the stated purpose of the visit in the light of the length of time that has elapsed since previous visits. A visitor should not, for example, normally spend more than six out of any 12 months in the UK.
 
In view of all the above, I do not consider that your actions are within the spirit of the immigration rules for family visitors. I note that you are widowed and that your two daughters and six siblings all live in the UK. Given that you have been spending long periods of time in the UK over the last few years, this raises doubts as to your true intentions.

Given all of the above and considering your application as a whole, I am not satisfied that you are genuinely seeking entry as a visitor for a limited period as stated by you, not exceeding six months and that you intend to leave the UK at the end of the period of the visit as stated by you (as required by Paragraph 41 (i) and (ii) of the Immigration Rules.”

In other words, the ECO was invoking the spent leave rule to cast doubt on the applicant's intent to comply with the provisions of Paragraph 41 of the rules.  The tribunal considered the case and had this to say...

1. There is no restriction on the number of visits a person may make to the UK, nor any requirement that a specified time must elapse between successive visits.
2. The periods of time spent in the United Kingdom and the country of residence will always be important.
3. Both the expressed purpose of the visit and what the appellant has done in the past and intends to do in the future is material, together with the length of time that has elapsed since previous visits.  In cases of this type, the appellant will be visiting a relative, often a parent visiting a son or daughter, often a son or daughter visiting a parent.  In the case of a parent visiting a son or daughter, the parent will often fully participate in helping in the house, providing child care.  In the case of a son or daughter visiting a parent, the adult child will often assist in care arrangements. None of these activities, for that reason alone, will take the individual outside the definition of a genuine visitor.
4. The links that the appellant retains with her country of residence will be a material consideration.  The presence of other family members will be a material consideration.
5. The Tribunal is required to ascertain what is the reality of the arrangement entered into between the appellant and the host in the United Kingdom.  Is the reality that the appellant is resident in the United Kingdom and intends to be for the foreseeable future?
6. The issue may be approached by considering whether the reality is that the appellant is now no more than a visitor to her country of residence as the purpose of the return home is confined to using his or her presence there solely as the means of gaining re-admission to the United Kingdom.
7. This does not preclude the appellant from remaining in the country of residence for the least amount of time sufficient to maintain her status as a genuine visitor.
8. Family emergencies, whilst likely to result in a longer visit than the established pattern, should not be regarded as taking up residence without adequate supporting evidence to that effect.  Thus, the pregnancy of a daughter or daughter-in-law or the aftermath of the birth might explain a more-protracted stay (within the 6-month duration of a single permitted visit); so, too, a serious medical condition. 
9. There may be comparisons with the person who owns homes in two different countries.  Is he resident in both or a visitor to one of them?

To make a long story short, the appellant won the appeal.  What we learn from this case is that guidance is simply guidance and not the law.  As a side-note, we have to reflect with sadness upon the government's recent decision to curtail appeal rights for family visitors.  As shown by the above case, justice would have permanently eluded the applicant and caused the unfair and illegal loss of family relationships.