Please feel free to explain where the methodology is flawed.
https://en.wikipedia.org/wiki/Democracy_Index#Methodology
From your link:
"Investment analyst Peter Tasker has criticised the Democracy Index for
lacking transparency and accountability beyond the numbers. To generate the index, the Economist Intelligence Unit has a scoring system in which various experts are asked to answer 60 questions and assign each reply a number, with the weighted average deciding the ranking. However, the final report does not indicate what kinds of experts, nor their number, nor whether the experts are employees of the Economist Intelligence Unit or independent scholars, nor the nationalities of the experts.
[21]"
I don't know who Peter Tasker is but it's a very significant criticism IMO. Democracy is a complex and contested concept, and so are the terms being used to quantify it ("political participation" etc.) All difficult things to attach numbers to and the least we ought to expect before granting the Economist's exercise any legitimacy at all is full transparency about the process by which criteria and definitions are agreed upon and applied in each situation.
In the absence of such transparency, and given The Economist's strong ideological preferences, I'm going to assume that their experts skew towards liberalism, and liberalism's tendency towards abstraction and formalism. By that I mean, liberals tend to be satisfied with e.g. formal equality before the law, discounting the effects of economic inequality; formal rights to free expression, ignoring the power structures that limit actual access to expression, etc. This kind of formal approach is going to flatter British democracy (unsurprisingly, given the provenance of a lot of these ideas), which excels in formal egalitarianism and openness, and de facto secrecy and privilege.
For instance, formally our press is unusually free, with no statutory regulation at all and no formal ties to parties or individual politicians. According to liberal precepts (free market- free expression) it ought to be exceptionally diverse and pluralistic, holding power rigorously to account. In actuality, well. Formally, it is not possible for the wealthy to buy influence in the British system. In actuality, the parties are so interlocked with hereditary and commercial wealth that it becomes very difficult to establish the difference between graft and clientelism and ordinary governance. Formally, our democracy is highly participatory, based as it is on mass membership parties governed by internal democratic processes. In actuality the parties are organised by patronage networks and ordinary members have almost no say in important decisions.
I could go on. The Democracy Index is basically a political weapon used to agitate for light touch regulation, and more broadly, to flatter certain kinds of western liberal democracies. Britain meanwhile is a very effectively managed managed democracy, IMO. Certain regimes need to imprison a lot of journalists and opposition politicians to achieve the kind of results our ruling class accomplish with little more than private schools, the honours system, an insane Australian billionaire and the annual Spectator garden party.