Then, the answer to the initial question is "yes":
Climate change will likely bring more rain to the UK.
A 4.9% increase seems like a rather small overall change.
However, the overall amount of precipitation over the year does not allow us to deduce the variation in precipitation over the seasons. Since precipitation varies over the year, we suspect that the increase in precipitation is not spread evenly over the year. If this is not the case, what would the pattern be?
Changes in precipitation patterns are likely to vary from month to month
Considering rainfall intensity and variability between years
The monthly precipitations alone do not provide the full picture,
as rain intensity is critical to understand the impact of rain on
human activities. The number of days with rainfall above 20 mm would
also be a useful indicator, since 20 mm is the threshold beyond which
precipitations are considered very heavy.
The variability in precipitations is quite high, and monthly precipitations
from one year to another might vary significantly. Therefore, even though
monthly precipitations are projected to increase during certain months,
it doesn't mean that during these months, there will always be more rain
than what was observed historically.
Caveats
Here, the median of the results from an ensemble of climate change models has been
used, after reading on the Climate Knowledge Portal that: "The median is a fairly
robust measure as it reduces the lower quality simulations of precipitation still
prevalent in many models". This means that 1/ uncertainty is fairly high when it
comes to the results of the models, and 2/ if we need to consider the worst-case
scenario, we should directly use the models that result in worst-case situations
for the UK, not only the median of the results from all the models.
Another limitation is that we consider the UK as a whole, while climatic
conditions have spatial variability as well. Regional rainfall are for
example influenced by the distance to the Atlantic Ocean and latitude.
Conclusion
Back to the initial question: Yes, climate change is projected to bring more rain to the UK on average by the end of the 21st century (4.9% increase). The rainfall pattern is also expected to change over the year, and this could potentially
lead to more intense rainfall, and longer dry spells.
Further investigations would be needed to better understand the potential impacts on human activities, especially in worst-case scenarios. These investigations should in particular include rainfall intensity, spatial variability, and the
climate change models considered.