Even if the EU had been able to create and maintain a common trade position prior to Brexit, the loss/partial loss of the UK within the Union will make it difficult for the EU to continue with business as usual for at least a short period of time. The uncertainties surrounding the departure of the second largest market within the EU means that EU negotiators have to reconsider their own market positions in nearly every single sector.
To launch negotiations on a free trade agreement with Singapore (or any other country) would mean starting to build a house without a clear foundation. No sensible partner would want to do such a thing. Instead, potential trade partners will want to wait until the specific terms and conditions of Brexit are sorted. Then, and only then, will it be possible for the UK to figure out what sort of obligations can it take up with the EU, at the WTO, and with potential trade partners.