How hard is it to get admitted to a PhD programm in UK/Ireland having specialist's degree from a mediocre Russian university? I am going to study "Bioengineering and bioinformatics" for the next 5 years and plan to pursue a scientific career afterwards. My family does not have much money to support me studying in cities like Moscow and Saint-Petersburg, so I chose a university with the best cost/prestige ratio(Mordovia State University). I am worried that the type of my diploma (specialist) and mediocrity of the university will decrease my chances of getting admitted so much that hard work won't be able to offset that (grades and research experience won't be an issue, I invest all my time in studying). I know that 5 years is a lot of time and I haven't even started to study, but I don't want to find out one day that my degree is useless and I won't be able to achieve my life goals.

So the main questions are:
How is the specialist's degree in such a field perceived in UK/Ireland?
How much will mediocrity of my university affect chances of getting admitted to a PhD program in a more or less good university?
What is more important in the admission process anyway, prestige of a university or hard work and passion that a candidate has?
tl;dr: Don't do this.

Long version: Studying in a second-class university for a 5-year long program will significantly reduce your chances to get admitted to a MSc/PhD program in UK, Europe and US. In particular:


The "specialist" programs are not known in western world. While a specialist diploma from MSU could be recognised by some Universities as a MSc degree and allow admittance to a PhD program, a similar diploma from unknown universities will be only recognised as an evidence of BSc-level education or not recognised at all.
The educational program in Mordova University is likely to be outdated and the assessment standards are likely to be low. It will be very difficult for you to keep yourself motivated through all 5 years. Inevitably, people get sidetracked from such programs into self-education and tend to become IT specialists or self-learnt coders rather than scientists.
Your current level of English is decent; it is likely that a second-class University program will not help you to improve you language skills above your current level. 
It is very likely that lecturers in Mordova University are not really involved  in international research. You will not obtain essential understanding of how the research is done in the western world, and this could significantly limit the scope and success of your applications.


Suggestion: Try to get yourself a stipend/scholarship/loan and get yourself to a decent program in Moscow / St. Petesburgh. Alternatively, search for any BSc program which admits you in any EU country. 

Remember, 5 years of your life is a huge commodity. If you are going to spend them on education, make sure this time is not wasted. Good luck.