You're mostly right. There are other differences between Sweden and GB - class system bolstered by exclusive schools for rich kids, size and density of population, Thatcher killing off trade unions, other history, ... etc., et.. - but, yes, there's a peculiar selfishness to British culture that reflects very badly on us.
I'd like our society to be more highly taxed, not least to assuage my own guilt as a boomer who's had all the advantages - decent post-war council housing, free university education, working NHS, good pensions, etc., etc. - and then seen the ladders pulled up after people believed the lies of certain of their rulers and decided selfishness, after all, was a proper. basis for our lives together. (Bear in mind, too, we are overall better off than we were back then.)
I still hear people lauding Maggie Thatcher (there'll be a proportion of readers of this thread, I'll be bound), not realising selfishness and entitlement are not in any way a good basis for civil society. Personally, I'm all right ("Jack!") in material terms ... but I'd much prefer to be worse off financially and living in a society where, amongst other social goods, a mother (or father!) could take time off work to care for a sick child without financial penalty.