By socially conservative you mean I live in a nice owned house and in a nice area - I do not forget my council house roots, or indeed my two up two down house, my late father who was a miner and my trade union which retired I am still a member of - I have always voted labour , but only last time abstained, as I could not vote for Corbyn ...
I voted brexit like many many labour voters .........
No, that's not what the phrase means, it refers more to one's values on immigration, crime, nationality and other social issues (in America it covers things like abortion and gay marriage).