If we have left, then we will still need to negotiate a real deal with the EU.
It's far worse than that. We will have to negotiate a deal with every other country outside the EU too, because, the deal the EU had with Peru that included us will no longer include us, so we will have no deal with Peru. If we wish to trade with Peru, we will need a new deal.
And the deals we negotiate with Peru and other counties will be worse than the EU deal we have now, because y' know what, the bigger the customer, the better the deal you give them. The trade Peru has with the EU including us is for more than the trade with just us.
Brexit won't be done for years and years.