OK, well first let's get the Russell Group thing out of the way first. It's a vehicle used to help member universities market themselves. It is not a guarantee of quality, and many excellent universities are not members. The university which currently tops both The Times and Sunday Times Good University Guide 2024 and the Guardian University Guide 2024 is not a member of the Russell Group. Of the top 10 universities according to the Complete University Guide's University League Tables 2024, four are not Russell Group. It's absolutely fine to target top universities which have high grade requirements, but please don't focus exclusively on the Russell Group.
Some top universities (e.g. Oxford) place a lot of emphasis on GCSE grades, but even then their importance will vary depending upon the course for which you're applying. Others place less importance on them. For example, Bristol rank applicants based upon a combination of their GCSE grades and their A level grades (actual or predicted) - normally in a 20:80 ratio (this can vary depending on the course). This means that for Bristol, for example, A level grades are four times as important as GCSE grades.
I think your school counselor is placing more emphasis on your GCSE grades than the top universities themselves do, and has scared you unnecessarily. Set their concerns to one side. What subject to you want to study at university? Once you've decided that, take a look at some of the courses offered by different universities and see which seem of interest to you. Check their entry requirements (which will cover both A level and GCSE grades) on their web sites. If you're still concerned, then return to this thread with some specifics (i.e. course X at university Y) and people will be in a much better position to guide you.
(By the way, you school counselor is talking utter nonsense when they say that you "might not make into a Russell group uni" with those GCSE grades and your predicted A level grades. You might not, but it won't be because of those grades.)