The CPS also has warned Britain's current broadband infrastructure market appears anti-competitive and Ofcom should refer the issue to the Competition and Markets Authority later this month.
A Digital Communications Review is currently being carried out by the communications regulator Ofcom and is expected to be released before the end of the month.
Ofcom does not have the power to split Openreach out from BT, however.
BT has hit back at the claims branding the CPS "blog" as "under researched".
A spokesperson for BT said: "Unlike respected independent studies by Ofcom, the EU and others, this blog is under-researched and paints a false picture of UK broadband. It compares the UK to other countries based only on average speeds, whereas other important measures - such as availability of services, prices and take-up – place the UK well against important international peers. There is simply no evidence that broadband investment would be higher or competition fiercer if Openreach became a smaller, weaker, standalone company. How could it, when the UK already has more than 500 firms competing in this market and Ofcom sets 96% of Openreach prices to level the playing field for them all?"
The CPS compares a delay to the decision to carve out Openreach to the ongoing debate over runway expansion at either Heathrow or Gatwick airports, saying it postponing could be “detrimental to the UK economy and Ofcom must not follow in these footsteps”.
The report points to the separation of infrastructure providers from internet service providers in Singapore and New Zealand to support its argument.
BT argues that there are disagree that structural separation has been a great success elsewhere, saying: "They find that the few countries to try it have either higher broadband prices, slower roll-outs, much larger tax-payer subsidies – or a combination of all three."
BT’s competitors, Sky, TalkTalk and Vodafone, have campaigned fiercely over recent months for the regulator to advise that Openreach is made independent.
Although Virgin Media, BT Openreach’s competitor, has also publicly backed BT Openreach against calls for structural separation, arguing that structurally separating BT Openreach would deter investment in broadband improvements.
Increasing the nation’s broadband speed has been suggested at a possible solution to the productivity crisis currently facing the UK.
Broadband Infrastructure Group estimates that 42 per cent of small and medium sized businesses currently report experiencing problems with their internet connectivity, costing the British economy an estimated £11bn each year.