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.
Special Edition: Why Becoming An Independent Trading Nation is Harder Than Expected
Brexit also changes the relationships that the UK has with all of the existing EU trade agreement partners. These are not only the 58 existing free trade agreements, but also various preference schemes in place, mostly for least developed economies. It also means that the UK will have to reset trade relations with most of the rest of the global trade system, since the UK will need to re-establish its independent seat at the World Trade Organization (WTO). This is much trickier than it first appears.