Like other developed nations, Britain gives quite a lot of financial
and other aid to developing nations, especially in Africa, which were
former colonies. The giving and acceptance of aid, together with the
monitoring of how the aid is spent, also the activity of British NGOs
in the ex-colonies, may in some cases lead to the sort of
paternalistic relationship between Britain and the former colony,
which resembles in some ways the old imperialistic relationship.
Perhaps "retro-imperialism" might be a better term for this sort of
relationship than "neo-imperialism".
However, Britain's relationship with most countries in the
Commonwealth is much more complex, and varies from country to country.
The fact that the Queen is the Head of the Commonwealth, and is also
the Head of State of some individual Commonwealth countries (eg Canada
and Australia), may make it seem as though Britain still has the same
role as in the days of the Empire. But all in all I would not think it
fair to describe Britain's behaviour towards most Commonwealth
countries as "neo-imperialistic".
The questioner also mentions Europe and the USA. As far as the former
is concerned, there is certainly no imperialism involved; and as for
the latter many British people would regard America as the
neo-imperial power trying to impose its culture and policies on
Britain (and other nations) rather than the other way round.