Well if it were the ones from the aquarium, it’s a small enough group that they might potentially be able to sort something out, although it depends on how long they’d be staying in London for.
The obvious place to try and place them would be in Penguin Beach. But of course, as Gentoos live in a different environment to Humboldts, it might not pan out as hoped (besides the potential risk of conflict between both species, although they got along fine with Ricky for years despite his differences).
If the zoo is able to invest some money in a more permanent enclosure for them, the old Anteater Lawn would probably be a good space to develop. There’s at least some room there for a pool and areas for them to walk, and as it’s mostly grass there would be very little to demolish on the lawn itself. And as I said before, the Mappins has enough space to augment it for a number of different creatures, although it would be a very large and expensive space to develop for just a small number of penguins.
Now, if temporary, and I mean very temporary (so we’re talking maybe a week or less), it could be possible to stick them in the Penguin Pool. It would have to be stressed that it was a temporary move (and only if nowhere else is available), both due to the issues with the enclosure and the negative attention an extended stay there might receive.
And really, they’d need to at least put down some extra padding or something similar to reduce the risk of bumblefoot seen in its earlier inhabitants. On the plus side, they would get plenty of sunshine and more traversable space overall than they have in the aquarium, so I could imagine it being considered if there really was nowhere else to go.
I imagine this approach was also taken for the sea lions when they occupied their old pond in 2012, as it was disused (for that species) for a similar amount of time as the Penguin Pool has now gone disused. It was a temporary move from Whipsnade in order to clean their enclosure there, so the same considerations might have been made.
Either way, I don’t doubt London Zoo would think of a good solution, especially since they have a deeper knowledge of the exact requirements (and also of their many backstage areas).
It would be too warm to exhibit Gentoo penguins outside so they would need a purpose built refrigerated house, which is not going to happen at London. The cost of building and running this would prohibit this.