I saw that news item on the BBC website, very interesting. The story is that platelets (small cells - in fact too small to be real cells - in the blood involved in clotting) can inhibit the body's normal immune defence against metastatic cells, and inhibiting platelet action with aspirin means the immune system is better at removing those metastases.
Doctors these days tend not to recommend aspirin, really because it is a problem for anyone who has stomach ulcers, precisely because of its effects on platelets and clotting. If you have a tendency towards bleeding from ulcers, the last thing you want is to inhibit clotting. For most things ibuprofen or paracetamol are equally effective alternatives.
Interestingly that same anti-clotting property is a benefit to anyone who has a stroke, which is caused by a clot and will be exacerbated by further clotting. The best thing you can do for someone suffering a stroke (after calling 999) is immediately give them an aspirin.
Anyway, the effect of aspirin on platelets is irreversible - which means a dose can inhibit them for a couple of days. (If you ever take aspirin, you may have noticed how shaving nicks take longer to heal). Ibuprofen, which is a broadly similar drug, is different in that its effect on platelets wears off in a few hours - so it might work as well for helping cancer spread but you would have to take it more often. Paracetamol, which is a component of cocodamol, is a bit less effective against platelets and again wears off.
I think Sscrabble from your previous posts, you are currently on HT awaiting RT. HT should provide an effective brake on prostate cancer, including any metastasis, and obviously RT is designed to deal with all the known sites of cancer.
Having said that, if aspirin is as effective against your back pain as cocodamol then the new data suggests it might be worth considering for its additional anti-cancer effect. But you should talk to your doctor, your current treatment is obviously designed to be enough to work, and long term aspirin does have a significant risk of side effects.