Very obviously, if it's lashing with rain all day or the cloud cover is thick and constant, no panel is going to help much. However, whilst this fact is true, it's not actually very helpful in trying to determine what wattage it is worth installing. It's obviously equally invalid to assume you're going to get anything like peak output except on exceptional summer days. Either good/bad extreme isn't really very useful in sizing a solar panel, it's the marginal days that count. The fact is that the UK has a wildly variable climate, both with respect to seasons and day to day that mean the range of solar outcomes is a wide and continuous distribution - it is very obviously not a sun/no-sun binary distribution.
Consider the rough cases:
1) Beautiful summer's day.
2) Cloudy summer, reasonable spring/autumn day.
3) Average/poor winter's day.
In case (1), any half-sensible van solar panel will likely do, in case (3) no realistically van-sized panel will do much (get the alternator with DC-DC on!) but in case (2) which is actually pretty common in the UK, the difference between a 100w and a 300w panel, for instance, could be substantial.
To make this more concrete, consider this plot (from
http://www.iesisenergy.org/agp/Aris-Solar-paper.pdf) of nationwide solar production through the year.
It should be obvious from this that the distribution of daily solar outcomes is very continuous, and basing anything on the extremes is a bad idea. If we take a bit of a leap (likely they're rather optimistic for our van case given we don't have great control over orientation and placement and the plot above is nationwide so includes geographical averaging we don't have so our error-bars will be much wider) and actually use the capacity factors on the right hand side, I can calculate (very!) rough expected potential Ah generation for each of my three cases above for my 250w panel, using the equation:
daily_Ah = (250w / 12v) * 24h * capacity_factor
Case 1 - Beautiful summer's day (capacity factor = 0.16):
(250 / 12) * 24 * 0.16 = 80Ah
Case 2 - Cloudy summer, reasonable spring/autumn day (capacity factor = 0.08):
(250 / 12) * 24 * 0.08 = 40Ah
Case 3 - Average/poor winter's day, or a day of significant rain in any season (capacity factor 0.025)
(250 / 12) * 24 * 0.08 = 12.5Ah
These numbers, whilst probably a bit optimistic, do feel ballpark-accurate from my experience of using my 250w solar panel for wild camping over the last three years. It should be very clear from this that the size of the solar panel will make a significant difference in the range of seasons and power requirements that van campers do genuinely care about. To simplify, if you want to extend your wild camping through Spring/Autumn, putting on a decent amount of solar is a good idea. In winter, whilst solar will help to top up, expect to have to run the engine to fill in the gaps.
For my personal use, my 250w panel has been ideal.