How hard is it to get admitted to a PhD programm in UK/Ireland having specialist's degree from a mediocre Russian university?
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The educational program in Mordova University is likely to be outdated and the assessment standards are likely to be low.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.