It sounds good doesn't it? More British History being taught in schools to give people a better idea of our collective history which might contribute to a shared national identity. Unfortunately, from looking at the subjects mentioned in the Guardian article, "the Commonwealth and empire, the slave trade and conflicts such as those in Northern Ireland", I doubt the result will be anything so positive.
Firstly, that list of subjects suggests that they've decided to avoid the challenge of trying to compose a history syllabus that might actually help children understand the broad sweep of British history. If that were the objective surely the Industrial Revolution would take central stage? The Glorious Revolution?
In fact, I would be interested in the results of a survey which attempted to gauge popular knowledge of the Glorious Revolution; I would guess that only a tiny minority have even heard of it. Despite this lack of awareness, I don't think any serious historian would argue it is less important to the British national identity than the conflict in Northern Ireland. The focus in the subjects chosen isn't on those which are important to understanding British national identity but on stories of past ethnic strife.
Bear in mind that the teaching of these events is unlikely to be balanced either. I, and many others, take the view that the practice of slavery was near universal throughout human history until the last two centuries and that Britain was distinctive in making a moral decision to abolish it. Whether or not you agree with this perspective it is unlikely to even be represented in the way the subject is taught in schools which will briefly mention Wilberforce but focus on enshrining slavery as an explanation for problems of the contemporary black community and another example of white evil. A choice of subjects which is biased towards examples of ethnic strife will be further biased by a left-wing teaching profession which sees these events as the result of a general white evil. The history of empire will be even more vulnerable to this bias.
Combine a focus upon periods of ethnic strife with the perspective that these problems are caused by white, Anglo-Saxon, evil and you have a recipe for lessons about how we should accept immigrants because of how awfully we mistreated their ancestors. Instead of trying to teach British national identity they're trying the old strategy of trying to guilt the white British population into playing nice; this is not a novel strategy and doesn't have the most impressive record of success.
An attempt to teach British children where their nation comes from, what it has achieved as well as where it has failed and the events that marked its formation, would be both noble and important. By giving people an understanding of what made Britain you might give them a better idea of a national identity they can unite around. However, how can national harmony be promoted by focussing unduly upon events characterised by ethnic conflict? Who would want to unite around a Britain whose achievements are the conflict in Northern Ireland, slavery and oppressing colonial peoples?
I expect it will take a Conservative government to recognise that it is a better knowledge of our achievements as well as our travails that can bind us together as a nation.