The short answer to this is yes, which is why they provide such a wonderful alternative to the likes of dentures. Whereas dentures need to be messily fixed in place, and taken out each night so they can be cleaned, dental implants are permanently screwed into your mouth and the implant part itself actually fuses with the bone at the jaw in order to ensure that your new, artificial teeth are anchored in place just as securely as the rest of your teeth.
This does, for some people, raise the concern that, if they get a couple of teeth implanted, then all their other teeth fall out naturally, that they may be left with only the teeth which have been implanted and no others. However, implanted teeth can actually protect other teeth from damage by filling in the gaps left by lost teeth and also by facilitating bone growth (for an explanation on this please refer back to one of the other articles).
So, whilst you may lose more teeth as you get older, you can always have more dental implants fitted in the Manchester or London clinics; dental implants are the only way to put a smile on your face permanently.