Given below, are the final June statistics for Edinburgh, Gogarbank from all of the data which I have available which are:

Temperature (°C):

Lowest Min: 5.9 (on 5/6)
Highest Min: 14.4 (on 23/6)
Mean Min: 10.2
Min. Anomaly: +1.1

Lowest Max: 12.6 (on 13/6)
Highest Max: 27.3 (on 25/6)
Mean Max: 18.2
Max. Anomaly: +1.0

Ave. Temp.: 14.2
Temp. Anomaly: +1.1

Rainfall (mm):

Total for Month: 69.2 (112.5% of 1981/2010 average)
Wettest Day: 13.6 (on 2/6)
Rain Days: 14 (134.6% of 1981/2010 average)
Dry Days: 9
Longest Dry Spell: 2 Days (7/6 to 8/6, 24/6 to 25/6 inclusive)
Highest Number of Days without a single dry day: 7 Days (17/6 to 23/6 inclusive)

Sunshine Totals (hrs):

Total For Month: 114.1 (74.0% of 1981-2010 average)
Sunniest Day: 14.4 (on 1/6)
Sunless Days: 3

Conclusion:

The month of June was cooler than average for a while during the first half of the month, although it did eventually warm up with quite a notable hot spell during the latter part of the month. This resulted in June 2020 being warmer than average in the end, in line with every other month during this year so far.

June was also slightly wetter than average overall both in terms of the actual rainfall amounts, and in terms of the number of official rain days. Indeed, it was our first wetter than average month since February 2020, although it wasn't as wet here as it was in various other parts of the UK and it also wasn't anywhere near as wet during June as what all of last year's summer months were in this part of the world..

June was also a lot duller than average overall. It was our first duller than average month since February 2020, and our first significantly duller than average month since January 2020. In fact, June 2020 came very close to being our dullest June since 2012. Luckily, we got just enough sunshine on the very last day of the month to ensure that this wasn't the case and in the end, June 2020 was just very slightly sunnier than June 2017.

Here are my stats for June - comes out quite small so click the table link and then magnify and you can see in full size

Table

Here is the monthly map for rainfall. The temp and sunshine maps were on the blog earlier but seem to have disappeared. 

Very wet, except (as so often these days) for the far SE. It does feel like the mean NW/SE split has been even further enhanced in recent years.

. 

One air frost, none too warm.
Wet but not very wet and some short dry spells too.
I'm not sure how that Met Office chart shows us on 200% but the recent downpours were quite localised for example one day we had 17mm but at Rievaulx there was 42mm

Average temperature = 12.9°C; diff from climate av: -0.1°C
Average humidity = 85%
Average dewpoint = 10.3°C
Average barometer = 1011.4 mb
Average windspeed = 6.1 mph
Average gustspeed = 9.2 mph
Average direction = 268° ( W )
Rainfall for month = 128.2 mm (+45mm)
Rainfall for year = 319.8 mm (-42mm)
Maximum rain per minute = 1.0 mm on day 27 at time 18:07
Maximum temperature = 27.9°C on day 24 at time 16:19
Minimum temperature = -0.3°C on day 09 at time 04:41
Maximum humidity = 99% on day 19 at time 07:09
Minimum humidity = 38% on day 02 at time 17:03
Maximum dewpoint = 20.5°C on day 26 at time 19:25
Minimum dewpoint = -1.2°C on day 09 at time 4:41
Maximum pressure = 1027.1 mb on day 01 at time 07:44
Minimum pressure = 987.0 mb on day 06 at time 08:40
Maximum windspeed = 40.3 mph from 360°( N ) on day 06 at time 10:51
Maximum gust speed = 54.1 mph from 00°( N ) on day 06 at time 12:12
Maximum heat index = 29.4°C on day 24 at time 16:18
Avg daily max temp :17.2°C
Avg daily min temp :8.8°C
Growing degrees days :120.3 GDD
Total windrun = 3961.1miles
Frost days= 1
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Daily rain totals
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09.2 mm on day 3
06.6 mm on day 4
08.0 mm on day 5
13.0 mm on day 6
12.2 mm on day 7
04.6 mm on day 10
12.2 mm on day 11
25.8 mm on day 12
04.4 mm on day 13
05.0 mm on day 18
04.6 mm on day 19
04.6 mm on day 21
16.2 mm on day 27
00.8 mm on day 28