Tutoring is a good way of boosting English language capability provided it is regular and boosted in other ways (e.g. summer courses in the UK). There are many good native English-speaking tutors residing in Moscow and St Petersburg who can help with this.
What is more difficult to find in Russia is tutoring for pre-assessment tests (many schools – not just the elite ones – use these tests to filter candidates) and school entrance exams. These entrance exams are at ages 10, 12 and 15, and the academic level by age 15 certainly demands specialist subject tutors who are rarely available in Russia. If the student must study in Russia (rather than attending a UK school from an earlier age), one very effective solution is on-line tutoring. There is a wide range of highly experienced tutors in the UK who are experts not only in their subject, but also in using on-line learning tools to deliver sessions in the student’s home. We strongly recommend this for students living in Nizhny Novgorod, Krasnodar, Kazan, Ekaterinburg, Tyumen, Surgut, Nizhnevartovsk, Novosibirsk, Krasnoyarsk, Irkutsk, Novokuznetsk, Kazan, Samara, Ufa, Alabuga as well as Kiev, Odessa, Baku, Almaty, Astana etc.