This is just meant to be a starting point, of how that political evolution occurred from a laywoman's POV. Obviously considerably more things happened during the various governments, but it might help.
WW2 exposed appalling conditions and social divides with little likelihood that those returning from war would be prepared to go back to the status quo. Attlee's government was able to use a post war sense of being united to everyone's advantage and what was referred to as the 'post war consensus' was formed.
Much was based on the Beverage report for the reconstruction of post war Britain tackling "Want, Disease, Ignorance, Squalor and Idleness"
It included Keynesian economics, a broad welfare state, and a mixed economy and regulation to protect people, environment and state. There was general agreement to what the country needed, but not always about how to get it or who should pay for it.
One of the most fundamental differences was beliefs around trickle down wealth systems, egalitarianism and non egalitarianism, and financial mechanisms.
The 'consensus' held together reasonably up to the late 60's when Enoch Powells inflammatory speech in '68 divided many. Labour's 1968 Race Relations Bill was three days away from its 2nd reading, with the Conservatives seeking amendments weakening it.* It shouldn't be underestimated. Immigration had generally represented cheaper labour and less working security for the WC's, who Labour generally represented.
Going back to 1964; Wilson inherited a balance of payments deficit of £800 million from the Conservatives' use of 'Stop-Go' cycles and inflation issues.
His government suffered economic crisis, was refused membership of the then EEC and was forced to devalue the pound.
Taxes were increased and by '69 a balance of payments surplus had been achieved.
However, shortly after, inflation was at 12 per cent, and Wilson had earlier alienated many Labour party members with his handling of the National Union of Seamen's strike, and claims of communist influence on the union.
He lost the election, though quite narrowly, to Heath.
*Although Heath had sacked Powell as going too far in divisiveness, at the time there was much talk of those who agreed with Powell giving their votes to the Conservative party. Principled Conservatives wanted nothing of it, but it still expanded the vote, and taught other politicians in waiting something important.
Heath took us into the EEC (then sold only as a common market for trading) presided over the 1st miners strikes in '72, housing as a profit mechanism,
followed by the disastrous secondary banking crisis, which caused the bank of England to loose around £100 million, around the same time as the global 1973/74 stock market crash. Concurrently the Organization of Arab Petroleum Exporting Countries (OAPEC) implemented an oil embargo against countries who'd supported Israel during the Fourth Arab–Israeli War., (oil prices through the roof) He handled increasingly heated industrial relationships hostilely including the miners 'work to rule' actions and strikes in '74.
In Jan 74 all industry was put on a 'three-day week' to conserve fuel as we were running out of it. (your parents mutterings)
Heath confidently enough called a general election with a question: 'who governs Britain?' Politicians or unions?
There were no Black MP's, but there were increasing numbers of Black and non White union leaders and the press sought to make a point of it.
Heath was somewhat caught out by a hung parliament, the 1st for 45 years.
Wilson came back in with a very minority government, and settled the miners strike, but spent the next two years trying to pacify the by now militant workers and deal with further economic crisis, and most importantly a split warring Labour party. The pound collapsed and had to be bailed out by the IMF.
Inflation peaked at 25% in '75. Labour tried to control inflation after 1975 by annual fixed wage increases. Lower paid workers found it unjust, especially as dividends and profits rose. Labour tried to offer better working conditions, HSE, and gender and race equality., and industrial democracy, by having worker-directors in companies with over 1,000 employees. The Conservatives and businesses successfully fought against that, and the press whipped up race rhetoric. The theory of Labour versus the reality of what was happening, left
many workers feeling strikes and solidarity were the only way to change things.
Wilson resigned exhausted, and Callahan took over. By then strike action was everywhere, spread to general workers especially public servants.
We had the 78/79 'Winter of Discontent' where everything from fuel, & food distribution to rubbish collection and burials had been hit. (mutterings part 2)
Following the defeat of the Scottish devolution referendum, Thatcher tabled a 'motion of no confidence' in Callaghan's government. It passed by one vote (311 to 310) forcing a general election five months before the end of the government's term. They were basically caught on the hop in the middle of a monumentally disastrous period.
Thatcher had been successfully campaigning for some time with specific populist key policies on ending immigration, strikes, Socialism and Egalitarianism, and ideas around people being strivers and skivers and 'what was fair,' and timed her actions well.
"...call the Conservative Party now to a crusade. Not only the Conservative Party. I appeal to all those men and women of goodwill who do not want a Marxist future for themselves or their children or their children's children. This is not just a fight about national solvency. It is a fight about the very foundations of the social order. It is a crusade not merely to put a temporary brake on Socialism, but to stop its onward march once and for all"
Thatcher favored economists Milton Friedman and Friedrich Hayek policies, which opposed Keynes.
"There is no alternative" became her accepted mantra and outlived her.
Saatchi and Saatchi's "Labour isn't working" political poster, appearing to be a long dole queue (actors), changed British electioneering methods for ever.
New Labour fundamentally accepted neoliberalism, though that's quite an un nuanced viewpoint, mainly seeking to manage it, rather than transform it, and adopting many Conservative stereotypes against Muslims, Asians, the black community, young single mothers, youth, and promoting the concept that 'disabled people receiving benefits should “justify” why they were “taking money from the state” detaching itself from it's original ideology in the process.
Neoliberalism had became naturalized, and we'd entered an era of "vote for us, or you get them" rather than genuinely different political ideologies. What will appeal to the voters, had become the only way forward.
Both Capitalism and Neoliberalism are extremely good at changing superficial appearance and adopting apparently different clothing.