No the uk has no direct democracy. Parliament is sovereign not the electorate. Indeed before any referendum the uk parliament has to pass specific legislation binding itself to the result+. These petitions are a relatively new thing and have never (please someone jump in and correct me if I'm wrong) lead to anything meaningful. 100,000 signatures mean that it has to be considered for a discussion in parliament - it doesn't even mean the discussion has to go ahead and if it does a vote in parliament may not happen (filibustering happens on non-goverment initiated debates in parliament) and would not be binding anyway.

+ interestingly the EU referendum was technically only advisory - but parliament would be mad to ignore it.