Ferdinand - firstly don't be downbeat. Internships in consulting are not that widespread - certainly there are far more graduates hired by consulting firms each year than there are internships for those partway through a degree course. So this isn't something to sweat over - particularly as it sounds like you're doing something this summer that'll look credible on your CV.
In terms of securing a consulting job when you graduate, these are the main factors that come into play:
1) Which university you are at - and how many of the consulting firms actively hire from this university. Nothing you can do about this now, but firms have pretty defined lists of universities they will and will not consider candidates from. So make sure you've done your homework with the Careers Service at your university and know which firms genuinly recruit from there (meaning they've been on campus to attract candidates this last academic year and / or you can see recent graduates have joined them upon graduation). Then invest your time in finding out as much as you can about these firms and perfecting your applications for them (rather than wasting your time with firms where you will not pass their screening hurdle for first round interviews as they simply don't hire from your school)
2) Solidify your claim to be on track to secure a First. Consulting firms do look for strong academics and someone with a credible claim that they are expected to attain a first will stand a much better chance of landing interviews. Time invested in any other extra-curricular activities will pale into insignificance compared with getting the right grade. Most consultancies don't recruit below 2.1 grade so a candidate expected to get a first is very appealing as if they make an offer they are unlikely to be faced with the dilemma of whether to still employ you should you only get a 2.2
3) It's good to look like you have some outside interests / positions of responsibility, but this makes a marginal difference compared with the university you're attending and your grades record. Next most important for most firms would be any fluency in foreign languages you can claim. So if your university offers a course that would allow you to state your proficiency in a foreign language on your applications that would be useful. Other qualifications I would say are less useful.
4) The above are all really aimed at getting you some interviews. But the competition is fierce once you have got interviews and tons of undergraduates fall by the wayside because i) they haven't really done their research to fully understand what a career in consulting involves and ii) they've not adequately prepared for the case study interviews. If you were going to invest time and / or money in anything then I would invest it here and in securing your First. By interview time you should be in the position of sounding quite knowledgeable to the interviewer regarding what a career in consulting entails, what the pitfalls are, what you're hoping to get from such a career, etc. It's not appealing at all to be faced with a potential hire who clearly needs bringing up to speed on what the job is actually going to involve and what they might find frustrating if they were to get the job.
I hope this helps and good luck!