What's the densest alkali metal? This was asked in a school exam of mine, GCSE curriculum, exactly as it was worded on the title. I found this question a bit vague, and answered it francium, however of course francium is just an estimation. I couldn't be sure what the answer to the question would be, so can anyone give me some insight?
It's hard to tell what is the answer you were supposed to provide, but yes, generally speaking, you are correct.
According to CRC handbook of chemistry and physics [1, p. 4-14] (emphasis mine):

Francium, the heaviest known member of the alkali metal series, occurs as a result of an alpha disintegration of actinium. […]
Because all known isotopes of francium are highly unstable, knowledge of the chemical properties of this element comes from radiochemical techniques. No weighable quantity
of the element has been prepared or isolated.

As the result, the majority of physical properties of francium, including density, were obtained by extrapolation and not by direct measurements.
According to Bonchev and Kamenska [2], $ρ_\mathrm{calcd.}(\ce{Fr}) \approx \pu{2.9 g cm-3}$, which is in a good agreement with the trend for the measured densities across the group.
For comparison, the following data (NTP conditions) is collected from the table PHYSICAL CONSTANTS OF INORGANIC COMPOUNDS [1, p. 4-43]:
$$
\begin{array}{cl}
\hline
\text{Element} &amp; ρ/\pu{g cm-3} \\
\hline
\ce{Li} &amp; 0.534 \\
\ce{Na} &amp; 0.97 \\
\ce{K} &amp; 0.89 \\
\ce{Rb} &amp; 1.53 \\
\ce{Cs} &amp; 1.873 \\
\hline
\end{array}
$$
References

Haynes, W. M.; Lide, D. R.; Bruno, T. J. CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data.; CRC Press, 2017; Vol. 97. ISBN 978-1-4987-5429-3.
Bonchev, D.; Kamenska, V. Predicting the Properties of the 113-120 Transactinide Elements. J. Phys. Chem. 1981, 85 (9), 1177–1186. https://doi.org/10.1021/j150609a021.