No it doesn't. If the right was in charge of the government of the UK they wouldn't have needed to have a referendum or drum up support for it.

Here's perhaps a concrete example to help piece this together. I live in Ohio. Our state government is right-leaning, and controlled by the Republican Party. The Republican Party has an anti-abortion platform.

A couple of years ago, citizens got together, created, and then passed an amendment to the Ohio Constitution providing abortion access as a legal right.

The right is still in control of the government, and that is true regardless of who paid to support the referendum, or how it was voted.