Thinking more along the lines of 120VA, as Watts /= VA.
Take the following into account (rough calculations):
1. FX-888/D is rated for 70W.
2. Efficiency for a linear supply is about 60%.
So 70W/0.60 ~= 117VA, so a 120VA transformer would be appropriate. Found the following listing on eBay:
Toroidal Transformer 120VA 230V -> 2x12V / 1x24V ; Sedlbauer, RSO-861756. Physical dimensions are very similar (89mm diameter x48mm tall for 120VA vs. 85mmx34mm for the 60VA you linked).
Take some measurements to see if it will fit, as they use an EI type (won't matter for this use if EI or toroid, just needs to have sufficient ratings and fit the available space). Just measure the existing transformer from corner to corner, as well as the height to see if a toroid will fit. Height is less of a concern than diameter in this case, given the Hakko's enclosure dimensions.
Another alternative, is to find an appropriate step-down transformer (100W continuous rating would be sufficient, but if you mean to run other 120V gear, take that into consideration). Much easier to use, as it's just a matter of plugging the transformer into mains, and the 120V gear into the step-down transformer outputs. Won't even need to change any plugs.
Needs to be an actual transformer, not a wall wort looking thing that's using a circuit instead of copper + iron (transformer = true sine wave output; wall wort versions tend to have an approximated sine wave output rather than a true sine wave). Avoids problems this way.
Example:
300W Step Down Transformer (smallest appropriate type that would work for the lowest cost I could find on eBay).
Based on the two links I provided, the Step-Down is not only less expensive, but it could be more useful as well (i.e. ~ 200 - 230W available for another bit of 120V gear).
A few GBP more perhaps could provide you with a larger unit (especially if you find a nice one used), that saves you more money down the road if/when you come across a US model for the right price to your door (assumes it doesn't have a switchable/convertible supply via internal wiring already, as some do).