I'm not too keen on some of the info shown on that site, davholla. Laterals don't really come into it with blackcurrants, so I don't really think it's a site to recommend for info.
If your blackcurrant already has lots of stems coming up from soil level, it may be 2 or 3 years old when you bought it, so you may not have to cut it. If it doesn't have lots of stems, cut it and give a high nitrogen feed.
In my experience, whitecurrants are pretty slow growing and don't need a great deal of pruning. Follow advice for redcurrants when pruning whitecurrants, they are totally different from blackcurrants.