Which version is your unit - the old one with antenna in and antenna out next to each other, or the new one with sockets one above the other? (I am asking this in case it turns out to be relevant - I don't have a "new" unit to look at.)
How do I fit a new antenna in?
In my opinion, unless you are experienced in that kind of thing (soldering etc), or are prepared to gain those skills, you can't. If you do have the skills (or know someone who does), you should have a pretty good idea just from looking at the damage. You may be able to use a part salvaged from an old TV, or solder a short length of aerial cable in place of the broken socket and fit an in-line socket to that.
If you don't know anyone who can help, and are not prepared to pay a repairer, there is nothing to lose by having a go yourself. For access, look at Commissioning, Disassembling, and Repairing an HDR-FOX (click)
Hi our box sits on the floor under the sofa so gets moved regularly when hovering.
That is very bad - not only for the reason you have discovered, but also for cooling. The unit needs a free circulation of air, and there will have been a lot of dust ingress. While you have it opened up, give it a good clean as well. In future, do not site it where it will have to be moved on a routine basis (never a good idea for anything with cables, and if you must then disconnect the cables first).