Cambridge/Oxford is almost completely off the tables due to competition aspect since most people would have done A - Levels with really high grades A*A*A*, etc. to get into that course so your at a disadvantage with that since its extremely exam focused so they'd assume you wont do to well there with the pressure they put you through. Atleast at an undergraduate level...
However, it is definitely possible to get into Russell groups with a BTEC Assuming you score good by the end of it so nothing less then DDD and your set for most places. In my case I did Applied Science Extended diploma with Maths A-LEVEL and did very well and got into Queen Mary's Aerospace engineering course and have graduated there. So you don't need anything else but Applied science and Math to get in.
But overall from what I can say a degree at a Russell group or Oxford/Cambridge does not mean anything for engineering at least... just go to a place where you feel comfortable and know you'll do well. Environment your in is key to doing well in an engineering degree so be honest with yourself when you go to open day instead of one choosing based on the name and prestige since the content is relatively the same everywhere at an undergraduate level.