We see that Sir Ivan Rogers, Britain's ambassador to the EU, is reported as saying that it could take until the mid-2020s to get a UK-EU trade deal in place.
That is certainly possible, because any such deal will almost certainly cover a wide range of issues, some of which will be within the exclusive competence of the EU, some of which will be shared competence between the EU and its Member States, and some of which will be within the exclusive competence of Member States. That means approval and ratification within the EU according to its own procedures, ratification by each of the EU's remaining 27 Member States according to their own constitutional arrangements, as well as ratification by the UK. So, procedurally, things may well be complex.
However, in today's world, trade agreements tend to be focused on the non-tariff barriers to trade, for example: standards; regulatory requirements; customs formalities and duties. Unlike the trade and cooperation agreements the EU has negotiated with third countries to date, where the aim is to move from divergence to some level of convergence, the UK and EU start from a position of convergence.
Therefore, it may be possible to agree the substance of a deal relatively quickly if the parties are willing.