Is it possible to travel to England with a Bulgarian ID card

While the UK has technically left the EU. It is, until the end of 2020, still in a transition period where most EU regulations apply. So for the moment yes you can use an EU national ID card to enter the UK.

However you should be aware that the UK is currently imposing 14 days of self-isolation on arrivals from abroad with very limited exemptions as part of their response to the COVID-19 pandemic. So you may well not be able to do what you intended on your visit. It is not clear how long these restrictions will be in-place for.

On the 10th of July 2020 England* is planning to exempt a number of countries from the quarantine but at the time of writing Bulgaria is not on the list. AIUI for the new UK quarantine rules what matters is not your citizenship but where you have been in the last fortnight, so (assuming you live in bulgaria) you could potentially spend a fortnight in a country on the UKs list of safe countries (assuming you can find one that will accept visitors from Bulgaria) before continuing to the UK.

You can find the list of exempted countries at https://www.gov.uk/guidance/coronavirus-covid-19-travel-corridors#travel-corridors-countries-and-territories-exemption-list. While much of the EU is included Bulgaria, Estonia, Latvia, Portugal, Romania, Slovakia, Slovinia and Sweden are not.

The list is also subject to change, Spain was initially on the exemption list but was removed after a spike in cases there.

* Rules for other parts of the UK will apparently "be published by the devolved administrations".

EU citizens can enter the UK on a national ID card, no matter how they travel.

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For now (at least until 2021), you're safe to use your Bulgarian ID card to travel to England.

If you're a visitor/tourist/newcomer, the government is intending to stop accepting ID cards from new arrivals later on (I can only assume it will be from 1st January 2021 - end of transition period, or from 1st July 2021 - after EU Settlement Scheme application deadline, it is not officially confirmed when).

If you live in the UK and have a pre-settled or settled status, you can continue to use the ID card until at least January 2026.

UK Government:

Crossing the UK border

Until at least January 2026 we’ll continue to recognise identity cards used for travel by EU citizens and their EU family members who are both resident in the UK before the end of the transition period and hold status under the EU Settlement Scheme. We will also recognise ICAO compliant identity cards from this group beyond 2026.

For newly arriving migrants, we intend to phase out the use of insecure identity documents and will set out further details on this shortly.

Another government source:

What you’ll need to enter the UK

There will be no change to travel document requirements this year. We may stop accepting national ID cards for entry to the UK for EEA and Swiss citizens after 2020. We’ll announce further details, including the date for this change, in advance to allow travellers good time to plan their trips.

If you begin living in the UK before 31 December 2020 and have status under the EU Settlement Scheme, you’ll be able to use your EEA or Swiss national identity card to enter the UK until at least 31 December 2025.