Native British people are not nor,ally offended by any stereotypes as they themselves rather think that it is funny, and this I can say about most of mainland Britain.
The ones who are easily offended tend to be the people who have come into Britain from elsewhere who consider themselves British because they have lived here for a good while, but not long enough to realize that the British (Those of us who "Get" what being British is) will laugh at themselves as it is who we are and how we naturally react.
Admittedly there are those who do not laugh at themselves because they are either full of self induced pride or they are bitter with unforgiveness, but they do not represent what being British is all about.
Remember that in most parts of the UK, if people joke about you in a harmless way it is their way of accepting you as a friend.
Parts of the UK do have different humour then others. The very Welsh parts of Wales which are the tough farming types tend to not laugh at some things that most of us would find funny, but if they hear about someone who has lost money or had an unfortunate event in an amusing way they will be chuckling about it for days! (Their humour differs a little from others because they have had to endure a tough life where their work becomes their life with 14 to 18 hour working days 7 days a week and may not see a day off for a month or two, so if they are out and about it will be to get supplies etc rather then to relax. Their work may not seem too intense to some but it is a continual work that is constantly there so they work exhausted so their humour tends to reflect this).
But apart from a few exceptions, most of us in Britain would laugh with you and certainly would not be offended.
The big problem is about the UK is that with the TV news channels, they have policies to promote ethnic diversity where many of the people employed have not lived in the UK long enough to adopt the UK ways into their character (As this takes a good few generations to do) and so we get the oppinions of those who are easily offended by anything that slightly questions their "Britishness" and they are the ones with agendas to push through laws by raising awareness of certain aspects they see as issues, and it in no way reflects what most of the British people are like as a whole and this is sad because it is destroying the very Character of Britain and creating an uncaring and callous atmosphere which is why so many peoples now live their lives in rebellion to the government and are not supportive where in the past governments had the upmost support here in the UK.
It has nothing to do with accepting ethnic minorities into the British culture as Britain always has had many different races living here.
It is the fault of pushing an agenda that does not represent the majority of the British people.
A classic example of this has been in the news lately regarding covid where they have been making news reports saying that unfortunately one will not be able to take ones holidays abroad this summer and isn't it terrible we are not going to be able to do that. They are soo out of touch with how the average person in Britain lives. I am average. I have never been abroad. In the area where I live only the wealthier people will go on holidays abroad, and most of us won't even have holidays other then day trips. The news media represent themselves and are soo out of touch with how most of us live here in the UK.
Many have passports but passports do not mean one uses them to go abroad, as these days people are forced to get a passport as a proof of identification or a drivers licence. That may have only used it once to go somewhere just to have the rare experience but are certainly could not regularly go abroad. The passport itself cost as much as they could afford to spend on a holiday these days.
The problem is that the media, and the government are formed of wealthy people. People can't stand as MP's unless they are currently doing ok for themselves which creates a scinario where some of them are already out of touch with how their constituents live. It is no ones fault. It is just the way things are. (And I realize that MP's do amazing work helping those with needs, but there is a difference of understanding between a person who sees those who struggle, and a person who is in the position of struggling, and unfortunately our laws and rules are based and made by those (In good will) who really don't know what it is like to live an average or below average lifestyle.
So do not look to what our press is saying or trying to portray about British people being easily offended by jokes being made about them, as most people in the UK will laugh with you and as a sign of effection as they get to know you, will have fun by noticing things about your character too!
After all. It is the British way!
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PM only.