I'm from Brazil, and I've been working in Lithuania for around 4 months (I could stay in Lithuania without a visa for 90 days in a 180-day period).
For reasons that are not relevant, I didn't apply for a visa in Lithuania, and my 90-day period has passed. Now, I'm illegally in Lithuania, but I am planning to go to the United Kingdom for 2–3 weeks to apply for a national D visa in the Lithuanian Embassy in London. I've dealt with all of the paperwork in the migration office in Lithuania, they know I'm here illegally, and I'm leaving voluntarily.
My problem is that, from what I heard from some of the migration officers, I might be stopped in the UK and not be let into the country, even though it doesn't belong to the Schengen Zone, even though Brazilian citizens can be in the UK for 6 months.
My question is if the mentioned facts are true, and what I can do to have no problems going to UK from Lithuania, while not being allowed to travel in Schengen countries.