America occupies parts of the Middle - east and after ten years becomes the most reviled and hated nation for those peoples. But the Brits stuck around for centuries and nothing like that hatred is ever seen in the former colonies. What gives?
I want to extend this to India, Australia and other colonies.
Was the reconciliation between the UK and its former empire a "natural" development. Or a conscious effort by statesmen and diplomats. And on the contrary, did certain actors in UK actively try to sour relations, or hinder reconciliation, trying to take back the empire?
TL;DR: The colonies were colonised and built up with imported citizens, while the Middle East was invaded/interfered/intervened in by America, with no lasting colony established.
I'll answer in the context of New Zealand, because it's the only country I have any personal experience of this in. I don't know that it can be applied in Australia, which is the most similar former colony to us.
The process of colonisation requires the movement of people from the colonising country to the colony, which in turn means the indigenous population will be displaced. This is a common theme, with First Nations peoples and Native Americans being moved out of their regions to make way for white settlement. In New Zealand, this occurred with Māori, in the form of land seizures in violation of the Treaty of Waitangi, which had been signed between some Māori chiefs and the British Crown in 1840.
This creates two groups in the colony: the indigenous and the settler. The settlers were largely of British extraction, with a communal attachment to Britain formed by their shared heritage. Britain had provided the defences for the colony in its early years; the settlers which allowed expansion and connection of early settlements into a more fully formed colony; and the investment which drove the early economy. British presence in New Zealand was strongly felt by the early settlers, and their descendants maintained that connection.
Māori were displaced through the settler presence, and the high flow of immigrants meant that the population numbers skewed in favour of the newcomers. This has continued into the modern era, and the Māori population now sits at around 15% as of 2013.
The two major groups in New Zealand then are Māori, who are the only ones likely to have strong feelings against Britain; and Pākehā, who have a strong cultural connection and benefited from the actions of the Empire's agents. The disparities in population and representation skew how these views are portrayed. I'll talk about public voices rather than private, because it's hard to speak for individuals without getting very anecdotal.
Pākehā are the dominant majority, both in parliament and the media, and the views of the British Empire most often reflect that group. Britian isn't viewed as a parent or home nation as much anymore, but it's still a major destination for young Kiwis on their OE, and elements of British culture are still visible here.
Māori representation comes through politicians, either in parties, from the Māori seats, or through specifically Māori political parties and movements, like the Māori and Mana parties, and the Kīngitanga. These groups do not speak for all Māori, but they do advocate for redress and compensation for historical wrongs. Despite them being professional political bodies, they have at times ventured into 'hatred' of Britain.
I'll give as an example of this one politician in particular. Hone Harawira, a prominent Māori activist, entered politics in 2005 with the formation of the Māori party. The party had formed in protest of government land policy. In 2009, Hone was caught up in a scandal for an email he sent with references to "white motherfuckers" and the rape of New Zealand by colonisers. In 2011 he resigned from the Māori party because he saw their relationship with the government as prioritising power over representation for Māori. He was returned to Parliament for the Mana Party in a by-election later that year, where he was almost immediately ejected for refusing to take a pledge of allegiance to the Queen. He was allowed to sit when he eventually took the pledge, but he said it in Māori rather than English.
The overall concept here is that the groups which would resent colonialism often don't have the voice necessary to dominate discourses in the former colonies. In contrast, those who benefited most from colonisation - the settlers and their descendants - have the dominant voices and positions. But the other aspect of this would be that instead of hatred or resentment being directed towards Britain, it's directed to the government which was installed by the British. New Zealand uses a Westminster political system, has laws that originated in Britain, and has used institutions which were adopted from British counterparts such as police, and land ownership practices which were not present in Māori society.
In summary, I'd say that the resentment remains, but it's not directed at Britain, but rather at institutions in the former colonies themselves. It's also tempered, because the colonised (in this case Māori) do have opportunities to operate from within the system to effect change, whereas the example you asked for a comparison to in the Middle East does not. There's no Representative for the 4th district of Iraq or Syria in Congress.
This is by no means a complete answer, because this is an enormous question. If you have follow ups, feel free to ask.