Well I suppose we could start by having a written constitution rather than a uncodified constitution, otherwise, it seems to me, once they bring in legal measures as acts and statutes and then the public gets used to an idea, it is not long before it gets baked into case law and then we're as good as fucked once it is accepted as common law.
Other than that, I suppose we could cross our fingers and hope for the best, like we did in the days before we had a constitutional monarchy, we would cross our fingers and hope we wouldn't get a shitty king. Well we don't need protection from our monarchs (as far as I can tell), we now are in dire need of protection from our government (and other "friendly" governments by extension).
Our customs and traditions have done well for us, its amazing to me we got this far, but maybe its time to get a bit more serious about our protections of rights and have them baked into common law.
I suppose there is a bit of irony that the protections we now seek from those who govern us are actually baked into the EU, but our country seems to be half in and half out (I'm a little angered I have to have cookie warnings on my web properties because of EU directives and yet my basic little right to privacy my grandparents generation helped put into the UN is not even taken seriously, never mind the EU equivalents).