You are completely wrong, to the extent of sounding like you're living in a parallel universe. The UK government was so strongly against Brexit at the time that

You are completely wrong, to the extent of sounding like you're living in a parallel universe. The UK government was so strongly against Brexit at the time that not only was it formally and officially committed to the campaign to remain but the moment it became clear the government had lost, the Prime Minister and Chancellor both resigned. This is all a matter of incredibly well documented public record.