Peter and his team are great. They really have the right experience and sensitivity preparing visa applications for tech talent. It took for my EB1a application 8 business days to file. I have recommended him to my friends looking for visas.
Bulgaria is in the European Union since 2007. Your dad is eligible to work in any of the 28 Member states without any restrictions. Why did you not consider this yet?
Because people have lives. You can't just pack up and leave normally speaking. Also, being from Romania or Bulgaria is not exactly treated as a preferential attribute when trying to locate work in other European countries. It shouldn't matter but it does.
So even if there are no legal restrictions there are plenty of barriers.
I don't think it's primarily the distance. It costs less than $200 to travel from Sofia to London by bus. This is less than half the median monthly income.
However, getting a job in London or another city will take time, and the cost of essential services like accommodation and public transport will quickly add up.