Well we can vote to rejoin the EU, sure, if all 27 other countries want us back, and if we join the Euro, and join the Shengen border free zone. And pay the full contribution without the rebates we negotiated. Personally I think we should do all that, and get over ourselves and stop being an awkward antagonistic special snowflake in Europe.
Europe is massively more democratic than it is perceived in the UK. The commission is headed by 28 representatives appointed by their democratically elected governments (albeit appointed to act in the interests of Europe) https://en.wikipedia.org/wiki/... the European parliament is made up of MEPs voted in directly. The council is the elected heads of state of the member countries. Junker was the first president of the commission elected to the post by the elected European parliament.
There is a reasonably plausible democratic path to everyone involved, naturally there are lots of civil service type staff employed by the whole thing, and it is a bloated gravy train of bureaucracy, but that in itself is reformable and not undemocratic.