What do you mean? You can only hold people accountable for their own sins, not the sins of their forebearers.

I think you mean "should" not "can", but regardless the past british government is not a forebearer of the current british government in the typical sense of the word. It is not a separate "person" but a continuous entity

Furthermore, hold responsible in this context means basically to acknowledge that the past actions were wrong, which is a pretty low bar as far as responsibility goes.

There is an argument that they do, as you cannot hold someone guilty for actions that they did not undertake.

At some point all of the criminals who did the thing in the past are dead.

Institutions can't act, because they have no brains or hands: only human beings can. You can't convict an institution of a crime, nor put it in prison.

Our entire society is based around the notion that institutins are separate legal personalities, distinct from the people that make them up. They can take on liability, sign contracts, be sanctioned by courts, etc.

Besides, we're talking moral responsibility not legal.

Yes, but that's a legal fiction. They can't act, neither can "our society" or "the government".

The only entities that can take actions of any kind are human beings.