The democratic deficit is not the UK Parliamet, it is the EU Parliament
I would argue that the first past the post system used by the U.K. to elect MPs to the House of Commons is, by modern standards, a deficient system.
In areas where one party normally dominates (normally described as ‘safe seats’) there is absolutely no incentive for any voters to turn out to vote for opposition parties. For most of my life, my vote for my local MP has made no difference whatsoever.
It’s normally considered funny or amusing when a serious politician loses their deposit in an election. But really, it’s a sad demonstration of how bad our system is.
Then we have the House of Lords. This revising chamber does have one advantage, at least it may have some people who actually know about the subject that is being debated, as they have come from real world professions/jobs. But it’s made up of members that are hereditary peers (92) or peers that have been appointed, or by official function, no member is ever subject to an election. So there is absolutely no democratic representation here whatsoever.
The system that was used for electing MEPs was much better in my opinion. At least I could have a meaningful influence on who got elected. And hence there was a good chance that if I contacted one of them, I would be able to make my point without getting a load of dribble back as a reply.
In my humble opinion, part of the reason why turnout in the elections for MEPs was poor, was the lack of education of the voters on what MEPs did, and how the E.U. actually worked. Not helped by the abysmal media coverage.
Also, in the E.U. system, separate from the representation by MEPs, representatives of each country’s government have a say. Both in the executive branch (European Council) and in the legislative branch (The Council of the European Union).
Any new legislation or amendments to existing legislation are proposed by the European Commission. Then joint approval of the European Parliament and the Council of the European Union is required before any changes can pass.
The U.K. certainly had a major influence on the E.U. and I personally think that the U.K. benefited greatly from being a member.
As to the hog wash that the U.K. is poor, we are in the list of the top ten richest countries in the world, and often listed as number five or six based on GDP.