where they insist on checking everything, it's as much about making sure you've not been doing anything disreputable / in the clink
i've done some where they asked for dates and what dole office you were signing on at if you were unemployed. it gets more complicated if you were doing temp / casual work though, especially if the companies have disappeared or you can't remember who the heck they were - and if it's civil service then they may be able to cross check against your income tax records.
not sure that having had spells on the dole will be held against you - but telling lies might if you get found out...
and if by hmp you mean something civil service, their application process is pretty much (officially at least) competency based, so as long as you can come up with some good BS for whichever competencies they are selecting on, you should be ok - at interview it's "give an example of a time you did X" so one good example, even if it's from a short term job, may well be better than a crappy example from a job you did for years. (and read the competencies they say they want before the interview, as that is the sort of thing they will base the questions on)