I make a big effort to try and record addresses as they were at the time, but for someone who is not native to the UK this could seem complicated. I also realise not everyone would like to do it this way, each to his/her own, I'm just sharing what I do.
London - For example, I would record Islington as in Middlesex until 1889 when the county of London was formed. This remained until 1965 when Greater London was formed. The UKBMD
https://www.ukbmd.org.uk/reg/index.html site is great for helping with this. A key thing to remember with Registration Districts is that many contain(ed) parishes within different counties.
I come from Ipswich and record addresses until 1894 as within the parish, e.g. Myrtle Road, St. Helens, Ipswich, Suffolk. After then parishes were no longer responsible for administration which transferred to Borough Councils etc. So this becomes just Myrtle Road, Ipswich, Suffolk.
As stated above, where there is a hamlet I would record - Address, Hamlet, Parish, County, Country.
Unitary Authorities raise an interesting dilemma. However, they do remain part of a county for ceremonial reasons, thus I would record Peterborough as in Cambridgeshire. I think this helps position the place for non-native people.
Post codes are a nightmare, so I record them for current address as an additional attribute. The Post Office do not recognise administrative boundaries, also they are not static and can occasionally change, particularly where there are significant housing developments.