What do I need to travel to London during the scheduled Brexit transition date?

Nothing is certain about Brexit. May's deal which would have resulting in a transition period just got voted down in Parliament. This was followed by a confidence vote which the government passed, but it's still far from clear where we go from here.

What I think can be said is.

The UK is not a country that normally gets in the business of stopping people from leaving. It doesn't even have government-run exit checks. If services are running and you have documentation that is acceptable to the destination of that service you will almost certainly be allowed to board. In other words if a direct service from the UK to other EU countries is running I would be extremely surprised if you were unable to board it using an EU national ID card.

The worry is whether services will be running at all. Most likely even in the event of a "no deal" brexit some sort of arrangement will be made to keep services running but until such an arrangement has been agreed and ratified on both sides it cannot be guaranteed.

If you insist on doing this and things don't become clearer before you leave for the trip then I would advice you bring your passport with you. You probably won't need it but it gives you options in the event that it is not possible to travel home directly.

It has been confirmed that, in a no-deal scenario, EU ID cards will remain valid for entry at least until 2021.

So just bring your ID card as usual.

It’s quite amazing I am having to say this two months from the end of what was meant to be a two year period in which everything was sorted but…..nobody knows.

By default, if nothing further happens, then a 'no deal Brexit' is where the country is heading.

Though many of the more enthusiastic pro-brexit people like to say that this is all good and fine and anything bad about it is fear-mongering, as things stand at the moment it does look to cause quite a lot of disruption for travellers as nothing has yet been agreed on how UK air traffic control, airline safety checks, and immigration will fit in with the world following the elimination of most of Britain’s international agreements.

This is of course an absolute worst case. Even many of those openly calling for no deal don’t literally mean do no extra work and just leave without any agreements. Many of them fully recognise that we have to normalise our World Trade Organisation status for example (currently the UK cannot trade on WTO rules) and other common sense things like this.

I’d like to hope this worst case won’t happen. Given that a smooth orderly Brexit in March seems highly unlikely this probably means the whole thing being delayed.

But in these uncertain times… everything is a huge nobody knows.

Looking at the list of possible options and assuming all are equally likely then things remaining largely as they are for another few years at least and there being no disruption comes out on top.

But if the worst case comes to pass and the drawbridge is pulled up then there’s likely to be huge disruption for anyone flying in April. Even if the crazy legal situation of there being no basis for planes to fly is sorted within a week the airlines will take much longer than this to get their schedule straight again.

Since nobody knows it all depends how much of a gambler you are and what your personal predictions are for how things will go.

If you’re a pessimist then I wouldn’t risk booking a flight for summer at least.

If you’re an optimist then just live your life as you would if all this wasn’t happening.

While the other answers talk about the official requirements I would add that you should be prepared for a dynamic situation leading up to and in the days following Brexit. It's possible requirements could change with little notice.

If at all possible bring a passport as it's your best bet to get home smoothly.

Edit - Updated based on Crazydre response.

In the worst case, entering the UK with an EU passport might be a problem after March 29th, but it is hard to imagine why leaving would be a problem. The EU will let you in, because you have an Eu passport, and the UK would have no reason to hold you. In the absolutely, absolutely worst case they might remove you from the country (highly unlikely), but they wouldn't stop you.