You should be aware that Ilford has two strategies for fixing fiber-base paper. The "one-minute" regime is the one they promote, and is intended to fix quickly, in stronger fixer, so that the fixer does its job before soaking into the fibers of the paper base, thus making washing easier. Find the website on the Ilford sequence for optimum permanence for more info. Note that the wash aid plays a crucial role in the processing sequence.
The more traditional fixing regime uses a weaker dilution of fixer for a longer time and an appropriately longer wash time.
The "stronger" fixer Ilford recommends for their products is the 1+4 dilution, which is commonly known as "film strength" since it is the standard dilution for fixing film. If your brand of fixer has two different dilutions, one for film and one for prints, you could probably use Ilford's shorter fixing time and the accompanying regime. If not, you're likely better off using the longer fixing time and the longer wash.
The Ilford optimum permanence sequence seems designed around a one-bath fixing regime. Additionally, the capacity of the fixer is somewhat low: 40 8x10 prints for a "commercial" standard of permanence, but only 10 8x10 prints per liter for "optimum permanence."
My personal preference is for two-bath fixing using the weaker ("print-strength) fixer. I fix 1.5-2 minutes in each bath with a wash between. My capacity is 36 prints per liter of bath one, meaning I can fix 36 prints in two baths before discarding bath one, replacing it with bath 2 and mixing a new second bath. I find this a lot easier to deal with with larger prints (keeping the fixing time to 60 seconds with larger prints is hard) and more economical by about a factor of two than the one-bath optimum permanence regime.
Hope this helps,
Doremus