"House of Cards" (1990-95) and "Yes, (Prime) Minister" (1980-88) both feature subplots in which a British Prime Minister solves unemployment by reinstating military conscription. Was this attempted by, or a policy of, any real party in the UK during this period?

The important thing to remember is that reinstating 'National Service' has a pedigree in British politics as a policy positioning 'flare' that a government is taking a socially-conservative view towards issues around work/youth/crime/society. It harks back to the good old days, taps into a feeling of disorder, youth indulgence and lack of discipline as well as, perhaps, positive views of 'Great' Britain in years now past. It therefore has been mooted before and in a similar vein since.

As a viable policy position there were no real serious attempts by Thatcher to institute it indeed her early government ruled it out as did her late government however there are cases when it was acknowledged as a something.

There are a few cases where along this socially conservative grandstanding "the army would sort them out" mentality has come to discussion - this coincidently was a dismal failure and did not in reality see the light of day in any meaningful sense. In some ways it can be seen as a inspiration of the same ideas in the above programmes and there were certainly many suggestions from many of Thatcher's own party

It might be that the youth training scheme is a form of this, and in many ways it was dressed up along similar lines as a government led-programme to build up jobs for unskilled school leavers which would also instil a sense of discipline. Despite cries from the opposite benches and nudges from her own Thatcher deliberately avoided conflating this too much with conscription, emphasising the optional nature of the service. I would personally argue that this was more due to present political concerns rather than an economic stance. Thatcher's government is remembered for its economic conservatism but there was a similar force for social issues as well which tends to get forgotten as it is less popular today (section 28, emphasis on nuclear families etc.) and didn't really work. Therefore I would disagree that her reluctance towards turning this into a more militaristic conscription system idea stems from her policy objectives as this was an area where these contradicted. It is also important to note that Thatcher was expanding the role and remit of the state by this YTS. This is representative of a broader point, she was far more ideologically flexible than she, and our memory of memory has led on. Her efforts on the NHS can be described as postulating at best, education likewise (and again only increased the size of the state). While for nationalised industries she may wanted to reduce the role of the state but this was as much a balance sheet and 'low hanging fruit' issue as it was an ideological one. Her resistance to the idea of conscription seems to stem from a political understanding of the 'optics' of conscription (considering totalitarianism and fascism accusations were ever far away) and the ardent desire of the joint chiefs of staff not to have conscription - which would waste the limited funds they had for little material benefit.

Personally I would argue that while these ideas are not directly modelled on any specific policy it is drawing from an ideological milieu of the time. The political status of National Service as a go-to socially conservative solution matched with to the many-ills which were erupting in 1980's Britain pushing it into the discourse of the time which the writers tapped into